Answer
(a) $$AB=\left[ \begin {array}{ccc} 6&-21&15\\ 8&-23&19
\\ 4&7&5\end {array} \right].$$
(a) $$AB=\left[ \begin {array}{ccc} 9&0&13\\ 7&-2&21
\\ 1&4&-19\end {array} \right].$$
Work Step by Step
Given
$$
A=\left[\begin{array}{rrr}{1} & {-1} & {7} \\ {2} & {-1} & {8} \\ {3} & {1} & {-1}\end{array}\right], \quad B=\left[\begin{array}{rrr}{1} & {1} & {2} \\ {2} & {1} & {1} \\ {1} & {-3} & {2}\end{array}\right].
$$
We have
(a) \begin{align*}
AB&=\left[\begin{array}{rrr}{1} & {-1} & {7} \\ {2} & {-1} & {8} \\ {3} & {1} & {-1}\end{array}\right]\left[\begin{array}{rrr}{1} & {1} & {2} \\ {2} & {1} & {1} \\ {1} & {-3} & {2}\end{array}\right]\\
&= \left[ \begin {array}{ccc} 6&-21&15\\ 8&-23&19
\\ 4&7&5\end {array} \right].
\end{align*}
(b) \begin{align*}
BA&=\left[\begin{array}{rrr}{1} & {1} & {2} \\ {2} & {1} & {1} \\ {1} & {-3} & {2}\end{array}\right]\left[\begin{array}{rrr}{1} & {-1} & {7} \\ {2} & {-1} & {8} \\ {3} & {1} & {-1}\end{array}\right]\\
&=\left[ \begin {array}{ccc} 9&0&13\\ 7&-2&21
\\ 1&4&-19\end {array} \right].
\end{align*}
