Answer
(a) $$AB=\left[ \begin {array}{cccc} -2&-1&-3&-2\\ 4&2&6&4
\\ -4&-2&-6&-4\\ 2&1&3&2
\end {array} \right] .$$
(a) $$AB=\left[ -4 \right].$$
Work Step by Step
Given
$$
A=\left[\begin{array}{r}{-1} \\ {2} \\ {-2} \\ {1}\end{array}\right], \quad B=\left[\begin{array}{llll}{2} & {1} & {3} & {2}\end{array}\right]
$$
We have
(a) \begin{align*}
AB&=\left[\begin{array}{r}{-1} \\ {2} \\ {-2} \\ {1}\end{array}\right] \left[\begin{array}{llll}{2} & {1} & {3} & {2}\end{array}\right] \\
&=\left[ \begin {array}{cccc} -2&-1&-3&-2\\ 4&2&6&4
\\ -4&-2&-6&-4\\ 2&1&3&2
\end {array} \right] .
\end{align*}
(b) \begin{align*}
BA&=\left[\begin{array}{llll}{2} & {1} & {3} & {2}\end{array}\right]\left[\begin{array}{r}{-1} \\ {2} \\ {-2} \\ {1}\end{array}\right]\\
&=\left[ -4 \right].
\end{align*}
