Answer
(a) $$AB=\left[ \begin {array}{c} 3\\ 10
\\ 26\end {array} \right] $$
(b) $BA$ not defined.
Work Step by Step
Given
$$
A=\left[\begin{array}{rrr}{0} & {-1} & {0} \\ {4} & {0} & {2} \\ {8} & {-1} & {7}\end{array}\right], \quad B=\left[\begin{array}{r}{2} \\ {-3} \\ {1}\end{array}\right]
$$
We have
(a) \begin{align*}
AB&=\left[\begin{array}{rrr}{0} & {-1} & {0} \\ {4} & {0} & {2} \\ {8} & {-1} & {7}\end{array}\right] \left[\begin{array}{r}{2} \\ {-3} \\ {1}\end{array}\right] \\
&= \left[ \begin {array}{c} 3\\ 10
\\ 26\end {array} \right]
.
\end{align*}
(b) $BA$ not defined.