Answer
( a) $$AB=\left[ 12 \right].$$
( b) $$BA=\left[ \begin {array}{ccc} 6&4&2\\ 9&6&3
\\ 0&0&0\end {array} \right].$$
Work Step by Step
Given
$$
A=\left[\begin{array}{ccc} {3}&{2} & {1} \end{array}\right], \quad B=\left[\begin{array}{rrr} {2} \\ {3} \\ {0} \end{array}\right]
$$
We have
(a) \begin{align*}
AB&=\left[\begin{array}{ccc} {3}&{2} & {1} \end{array}\right] \left[\begin{array}{rrr} {2} \\ {3} \\ {0} \end{array}\right]\\
&=\left[ 12 \right].
\end{align*}
(b) \begin{align*}
BA&=\left[\begin{array}{ccc} {2} \\ {3} \\ {0} \end{array}\right]\left[\begin{array}{rrr} {3}&{2} & {1} \end{array}\right]\\
&=\left[ \begin {array}{ccc} 6&4&2\\ 9&6&3
\\ 0&0&0\end {array} \right].
\end{align*}
