Answer
a) $AB=\left[ \begin{matrix}
0 & 6 & 6 & 2 & 2 & 0 \\
0 & 0 & 1 & 1 & 5 & 5 \\
\end{matrix} \right]$
Work Step by Step
(a)
$\begin{align}
& AB=\left[ \begin{matrix}
2 & 0 \\
0 & 1 \\
\end{matrix} \right]\left[ \begin{matrix}
0 & 3 & 3 & 1 & 1 & 0 \\
0 & 0 & 1 & 1 & 5 & 5 \\
\end{matrix} \right] \\
& AB=\left[ \begin{matrix}
2\left( 0 \right)+\left( 0 \right)\left( 0 \right) & 2\left( 3 \right)+\left( 0 \right)\left( 0 \right) & 2\left( 3 \right)+\left( 0 \right)\left( 1 \right) & 2\left( 1 \right)+\left( 0 \right)\left( 1 \right) & 2\left( 1 \right)+\left( 0 \right)\left( 5 \right) & 2\left( 0 \right)+\left( 0 \right)\left( 5 \right) \\
0\left( 0 \right)+1\left( 0 \right) & 0\left( 3 \right)+1\left( 0 \right) & 0\left( 3 \right)+1\left( 1 \right) & 0\left( 1 \right)+1\left( 1 \right) & 0\left( 1 \right)+1\left( 5 \right) & 0\left( 0 \right)+1\left( 5 \right) \\
\end{matrix} \right] \\
& AB=\left[ \begin{matrix}
0+0 & 6+0 & 6+0 & 2+0 & 2+0 & 0+0 \\
0+0 & 0+0 & 0+1 & 0+1 & 0+5 & 0+5 \\
\end{matrix} \right] \\
& AB=\left[ \begin{matrix}
0 & 6 & 6 & 2 & 2 & 0 \\
0 & 0 & 1 & 1 & 5 & 5 \\
\end{matrix} \right] \\
\end{align}$
(b)
The graph for matrix A and AB is drawn as shown above. From the graph, it can be inferred that the shape of letter “L” has been changed because of matrix multiplication. The length and width of the letter “L” has increased.
