Answer
(a) $$AB= \left[ \begin {array}{cccc} 3&4&-9&11\\ 17&-4&14&4
\\ -5&0&3&-13\end {array} \right] .$$
(b) $BA$ not defined.
Work Step by Step
Given
$$
A=\left[\begin{array}{rrr}{2} & {1} & {2} \\ {3} & {-1} & {-2} \\ {-2} & {1} & {-2}\end{array}\right], \quad B=\left[\begin{array}{rrrr}{4} & {0} & {1} & {3} \\ {-1} & {2} & {-3} & {-1} \\ {-2} & {1} & {4} & {3}\end{array}\right]
$$
We have
(a) \begin{align*}
AB&=\left[\begin{array}{rrr}{2} & {1} & {2} \\ {3} & {-1} & {-2} \\ {-2} & {1} & {-2}\end{array}\right]\left[\begin{array}{rrrr}{4} & {0} & {1} & {3} \\ {-1} & {2} & {-3} & {-1} \\ {-2} & {1} & {4} & {3}\end{array}\right] \\
&= \left[ \begin {array}{cccc} 3&4&-9&11\\ 17&-4&14&4
\\ -5&0&3&-13\end {array} \right] .
\end{align*}
(b) $BA$ not defined.