Formulaic Maths Problems
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Let $A = \begin{pmatrix} -6 & -5 & -5 \\ -1 & -3 & 0 \\ 4 & -9 & 11 \\ -11 & 8 & 9 \end{pmatrix}$ and $B = \begin{pmatrix} 6 & -7 & 3 \\ 11 & -9 & -10 \\ -6 & -7 & -4 \end{pmatrix}$. Find $AB$.
Row 1, column 1:
Hint: Row 1 of $A$ is $\begin{pmatrix} -6 & -5 & -5 \end{pmatrix}$. Column 1 of $B$ is $\begin{pmatrix} 6 \\ 11 \\ -6 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0a0}}\hspace{40px}}~} \times \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0b0}}\hspace{40px}}~} + \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0a1}}\hspace{40px}}~} \times \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0b1}}\hspace{40px}}~} + \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0a2}}\hspace{40px}}~} \times \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0b2}}\hspace{40px}}~}$
$[-6] \times [6] + [-5] \times [11] + [-5] \times [-6]$
$= \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0p0}}\hspace{54px}}~} + \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0p1}}\hspace{54px}}~} + \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0p2}}\hspace{54px}}~} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0R}}\hspace{54px}}~}$
$= [-36] + [-55] + [30] = [-61]$
Row 1, column 2:
Hint: Row 1 of $A$ is $\begin{pmatrix} -6 & -5 & -5 \end{pmatrix}$. Column 2 of $B$ is $\begin{pmatrix} -7 \\ -9 \\ -7 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1a0}}\hspace{40px}}~} \times \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1b0}}\hspace{40px}}~} + \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1a1}}\hspace{40px}}~} \times \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1b1}}\hspace{40px}}~} + \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1a2}}\hspace{40px}}~} \times \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1b2}}\hspace{40px}}~}$
$[-6] \times [-7] + [-5] \times [-9] + [-5] \times [-7]$
$= \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1p0}}\hspace{54px}}~} + \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1p1}}\hspace{54px}}~} + \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1p2}}\hspace{54px}}~} = \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1R}}\hspace{54px}}~}$
$= [42] + [45] + [35] = [122]$
Row 1, column 3:
Hint: Row 1 of $A$ is $\begin{pmatrix} -6 & -5 & -5 \end{pmatrix}$. Column 3 of $B$ is $\begin{pmatrix} 3 \\ -10 \\ -4 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step5}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2a0}}\hspace{40px}}~} \times \class{inputBox step5}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2b0}}\hspace{40px}}~} + \class{inputBox step5}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2a1}}\hspace{40px}}~} \times \class{inputBox step5}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2b1}}\hspace{40px}}~} + \class{inputBox step5}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2a2}}\hspace{40px}}~} \times \class{inputBox step5}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2b2}}\hspace{40px}}~}$
$[-6] \times [3] + [-5] \times [-10] + [-5] \times [-4]$
$= \class{inputBox step6}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2p0}}\hspace{54px}}~} + \class{inputBox step6}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2p1}}\hspace{54px}}~} + \class{inputBox step6}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2p2}}\hspace{54px}}~} = \class{inputBox step6}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2R}}\hspace{54px}}~}$
$= [-18] + [50] + [20] = [52]$
Row 2, column 1:
Hint: Row 2 of $A$ is $\begin{pmatrix} -1 & -3 & 0 \end{pmatrix}$. Column 1 of $B$ is $\begin{pmatrix} 6 \\ 11 \\ -6 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step7}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0a0}}\hspace{40px}}~} \times \class{inputBox step7}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0b0}}\hspace{40px}}~} + \class{inputBox step7}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0a1}}\hspace{40px}}~} \times \class{inputBox step7}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0b1}}\hspace{40px}}~} + \class{inputBox step7}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0a2}}\hspace{40px}}~} \times \class{inputBox step7}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0b2}}\hspace{40px}}~}$
$[-1] \times [6] + [-3] \times [11] + [0] \times [-6]$
$= \class{inputBox step8}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0p0}}\hspace{54px}}~} + \class{inputBox step8}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0p1}}\hspace{54px}}~} + \class{inputBox step8}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0p2}}\hspace{54px}}~} = \class{inputBox step8}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0R}}\hspace{54px}}~}$
$= [-6] + [-33] + [0] = [-39]$
Row 2, column 2:
Hint: Row 2 of $A$ is $\begin{pmatrix} -1 & -3 & 0 \end{pmatrix}$. Column 2 of $B$ is $\begin{pmatrix} -7 \\ -9 \\ -7 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step9}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1a0}}\hspace{40px}}~} \times \class{inputBox step9}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1b0}}\hspace{40px}}~} + \class{inputBox step9}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1a1}}\hspace{40px}}~} \times \class{inputBox step9}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1b1}}\hspace{40px}}~} + \class{inputBox step9}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1a2}}\hspace{40px}}~} \times \class{inputBox step9}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1b2}}\hspace{40px}}~}$
$[-1] \times [-7] + [-3] \times [-9] + [0] \times [-7]$
$= \class{inputBox step10}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1p0}}\hspace{54px}}~} + \class{inputBox step10}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1p1}}\hspace{54px}}~} + \class{inputBox step10}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1p2}}\hspace{54px}}~} = \class{inputBox step10}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1R}}\hspace{54px}}~}$
$= [7] + [27] + [0] = [34]$
Row 2, column 3:
Hint: Row 2 of $A$ is $\begin{pmatrix} -1 & -3 & 0 \end{pmatrix}$. Column 3 of $B$ is $\begin{pmatrix} 3 \\ -10 \\ -4 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step11}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2a0}}\hspace{40px}}~} \times \class{inputBox step11}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2b0}}\hspace{40px}}~} + \class{inputBox step11}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2a1}}\hspace{40px}}~} \times \class{inputBox step11}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2b1}}\hspace{40px}}~} + \class{inputBox step11}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2a2}}\hspace{40px}}~} \times \class{inputBox step11}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2b2}}\hspace{40px}}~}$
$[-1] \times [3] + [-3] \times [-10] + [0] \times [-4]$
$= \class{inputBox step12}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2p0}}\hspace{54px}}~} + \class{inputBox step12}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2p1}}\hspace{54px}}~} + \class{inputBox step12}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2p2}}\hspace{54px}}~} = \class{inputBox step12}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2R}}\hspace{54px}}~}$
$= [-3] + [30] + [0] = [27]$
Row 3, column 1:
Hint: Row 3 of $A$ is $\begin{pmatrix} 4 & -9 & 11 \end{pmatrix}$. Column 1 of $B$ is $\begin{pmatrix} 6 \\ 11 \\ -6 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step13}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0a0}}\hspace{40px}}~} \times \class{inputBox step13}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0b0}}\hspace{40px}}~} + \class{inputBox step13}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0a1}}\hspace{40px}}~} \times \class{inputBox step13}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0b1}}\hspace{40px}}~} + \class{inputBox step13}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0a2}}\hspace{40px}}~} \times \class{inputBox step13}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0b2}}\hspace{40px}}~}$
$[4] \times [6] + [-9] \times [11] + [11] \times [-6]$
$= \class{inputBox step14}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0p0}}\hspace{54px}}~} + \class{inputBox step14}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0p1}}\hspace{54px}}~} + \class{inputBox step14}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0p2}}\hspace{54px}}~} = \class{inputBox step14}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0R}}\hspace{54px}}~}$
$= [24] + [-99] + [-66] = [-141]$
Row 3, column 2:
Hint: Row 3 of $A$ is $\begin{pmatrix} 4 & -9 & 11 \end{pmatrix}$. Column 2 of $B$ is $\begin{pmatrix} -7 \\ -9 \\ -7 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step15}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1a0}}\hspace{40px}}~} \times \class{inputBox step15}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1b0}}\hspace{40px}}~} + \class{inputBox step15}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1a1}}\hspace{40px}}~} \times \class{inputBox step15}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1b1}}\hspace{40px}}~} + \class{inputBox step15}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1a2}}\hspace{40px}}~} \times \class{inputBox step15}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1b2}}\hspace{40px}}~}$
$[4] \times [-7] + [-9] \times [-9] + [11] \times [-7]$
$= \class{inputBox step16}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1p0}}\hspace{54px}}~} + \class{inputBox step16}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1p1}}\hspace{54px}}~} + \class{inputBox step16}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1p2}}\hspace{54px}}~} = \class{inputBox step16}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1R}}\hspace{54px}}~}$
$= [-28] + [81] + [-77] = [-24]$
Row 3, column 3:
Hint: Row 3 of $A$ is $\begin{pmatrix} 4 & -9 & 11 \end{pmatrix}$. Column 3 of $B$ is $\begin{pmatrix} 3 \\ -10 \\ -4 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step17}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2a0}}\hspace{40px}}~} \times \class{inputBox step17}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2b0}}\hspace{40px}}~} + \class{inputBox step17}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2a1}}\hspace{40px}}~} \times \class{inputBox step17}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2b1}}\hspace{40px}}~} + \class{inputBox step17}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2a2}}\hspace{40px}}~} \times \class{inputBox step17}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2b2}}\hspace{40px}}~}$
$[4] \times [3] + [-9] \times [-10] + [11] \times [-4]$
$= \class{inputBox step18}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2p0}}\hspace{54px}}~} + \class{inputBox step18}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2p1}}\hspace{54px}}~} + \class{inputBox step18}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2p2}}\hspace{54px}}~} = \class{inputBox step18}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2R}}\hspace{54px}}~}$
$= [12] + [90] + [-44] = [58]$
Row 4, column 1:
Hint: Row 4 of $A$ is $\begin{pmatrix} -11 & 8 & 9 \end{pmatrix}$. Column 1 of $B$ is $\begin{pmatrix} 6 \\ 11 \\ -6 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step19}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0a0}}\hspace{40px}}~} \times \class{inputBox step19}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0b0}}\hspace{40px}}~} + \class{inputBox step19}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0a1}}\hspace{40px}}~} \times \class{inputBox step19}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0b1}}\hspace{40px}}~} + \class{inputBox step19}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0a2}}\hspace{40px}}~} \times \class{inputBox step19}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0b2}}\hspace{40px}}~}$
$[-11] \times [6] + [8] \times [11] + [9] \times [-6]$
$= \class{inputBox step20}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0p0}}\hspace{54px}}~} + \class{inputBox step20}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0p1}}\hspace{54px}}~} + \class{inputBox step20}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0p2}}\hspace{54px}}~} = \class{inputBox step20}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0R}}\hspace{54px}}~}$
$= [-66] + [88] + [-54] = [-32]$
Row 4, column 2:
Hint: Row 4 of $A$ is $\begin{pmatrix} -11 & 8 & 9 \end{pmatrix}$. Column 2 of $B$ is $\begin{pmatrix} -7 \\ -9 \\ -7 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step21}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1a0}}\hspace{40px}}~} \times \class{inputBox step21}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1b0}}\hspace{40px}}~} + \class{inputBox step21}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1a1}}\hspace{40px}}~} \times \class{inputBox step21}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1b1}}\hspace{40px}}~} + \class{inputBox step21}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1a2}}\hspace{40px}}~} \times \class{inputBox step21}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1b2}}\hspace{40px}}~}$
$[-11] \times [-7] + [8] \times [-9] + [9] \times [-7]$
$= \class{inputBox step22}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1p0}}\hspace{54px}}~} + \class{inputBox step22}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1p1}}\hspace{54px}}~} + \class{inputBox step22}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1p2}}\hspace{54px}}~} = \class{inputBox step22}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1R}}\hspace{54px}}~}$
$= [77] + [-72] + [-63] = [-58]$
Row 4, column 3:
Hint: Row 4 of $A$ is $\begin{pmatrix} -11 & 8 & 9 \end{pmatrix}$. Column 3 of $B$ is $\begin{pmatrix} 3 \\ -10 \\ -4 \end{pmatrix}$. Multiply in pairs and add the results.
$\class{inputBox step23}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2a0}}\hspace{40px}}~} \times \class{inputBox step23}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2b0}}\hspace{40px}}~} + \class{inputBox step23}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2a1}}\hspace{40px}}~} \times \class{inputBox step23}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2b1}}\hspace{40px}}~} + \class{inputBox step23}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2a2}}\hspace{40px}}~} \times \class{inputBox step23}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2b2}}\hspace{40px}}~}$
$[-11] \times [3] + [8] \times [-10] + [9] \times [-4]$
$= \class{inputBox step24}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2p0}}\hspace{54px}}~} + \class{inputBox step24}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2p1}}\hspace{54px}}~} + \class{inputBox step24}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2p2}}\hspace{54px}}~} = \class{inputBox step24}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2R}}\hspace{54px}}~}$
$= [-33] + [-80] + [-36] = [-149]$
Therefore,
$AB = \begin{pmatrix} \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr0c0}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr0c1}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr0c2}}\hspace{54px}}~} \\ \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr1c0}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr1c1}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr1c2}}\hspace{54px}}~} \\ \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr2c0}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr2c1}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr2c2}}\hspace{54px}}~} \\ \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr3c0}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr3c1}}\hspace{54px}}~} & \class{inputBox step25}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{Fr3c2}}\hspace{54px}}~} \end{pmatrix}$
$AB = \begin{pmatrix} [-61] & [122] & [52] \\ [-39] & [34] & [27] \\ [-141] & [-24] & [58] \\ [-32] & [-58] & [-149] \end{pmatrix}$