Answer
$\begin{bmatrix}-7&4\\7&-6\\12&-7\end{bmatrix}$
Work Step by Step
(a)$
\begin{align}
AB&=\begin{bmatrix}A\begin{bmatrix}3\\-2\end{bmatrix}
&A\begin{bmatrix}-2\\1\end{bmatrix}\end{bmatrix}\\
&=\begin{bmatrix}3\begin{bmatrix}-1\\5\\2\end{bmatrix}-2\begin{bmatrix}2\\4\\-3\end{bmatrix}&(-2)\begin{bmatrix}-1\\5\\2\end{bmatrix}+1\begin{bmatrix}2\\4\\-3\end{bmatrix}\end{bmatrix}\\
&=\begin{bmatrix}-3-4&2+2\\15-8&-10+4\\6+6&-4-3\end{bmatrix}\\
&=\begin{bmatrix}-7&4\\7&-6\\12&-7\end{bmatrix}
\end{align}
$
(b)$
\begin{align}
AB&=\begin{bmatrix}(-1)(3)+(2)(-2)&(-1)(-2)+(2)(1)\\
(5)(3)+(4)(-2)&(5)(-2)+(4)(1)\\(2)(3)+(-3)(-2)&(2)(-2)+(-3)(1)\end{bmatrix}\\
&=\begin{bmatrix}-3-4&2+2\\15-8&-10+4\\6+6&-4-3\end{bmatrix}\\
&=\begin{bmatrix}-7&4\\7&-6\\12&-7\end{bmatrix}
\end{align}
$
