Answer
a) $AB=\left[ \begin{matrix}
-10 & 12 \\
25 & -30 \\
\end{matrix} \right]$
b) $BA=\left[ \begin{matrix}
0 & 0 \\
9 & -40 \\
\end{matrix} \right]$
Work Step by Step
(a)
$\begin{align}
& AB=\left[ \begin{matrix}
3 & -2 \\
1 & 5 \\
\end{matrix} \right]\left[ \begin{matrix}
0 & 0 \\
5 & -6 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
3\left( 0 \right)-2\left( 5 \right) & 3\left( 0 \right)-2\left( -6 \right) \\
1\left( 0 \right)+5\left( 5 \right) & 1\left( 0 \right)+5\left( -6 \right) \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
0-10 & 0+12 \\
0+25 & 0-30 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-10 & 12 \\
25 & -30 \\
\end{matrix} \right]
\end{align}$
(b)
$\begin{align}
& BA=\left[ \begin{matrix}
0 & 0 \\
5 & -6 \\
\end{matrix} \right]\left[ \begin{matrix}
3 & -2 \\
1 & 5 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
0\left( 3 \right)+0\left( 1 \right) & 0\left( -2 \right)+0\left( 5 \right) \\
5\left( 3 \right)-6\left( 1 \right) & 5\left( -2 \right)-6\left( 5 \right) \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
0+0 & 0+0 \\
15-6 & -10-30 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
0 & 0 \\
9 & -40 \\
\end{matrix} \right]
\end{align}$
