Either the Dimensions of Two Matrices or the Matrices Themselves $$A = \left[ \begin{array} { r } 1 \\- 3 \\2\end{array} \right] ; B = \left[ \begin{array} { r } - 1 \\3 \\2\end{array} \right]$$

Multiple Choice

Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and
the product BA. If either is not defined, say so.
- $$A = \left[ \begin{array} { r } 1 \\- 3 \\2\end{array} \right] ; B = \left[ \begin{array} { r } - 1 \\3 \\2\end{array} \right]$$

A) $\mathrm { AB }$ is not defined; $\mathrm { BA }$ is not defined
B) $\mathrm { AB }$ is $1 \times 1$ ; BA is $1 \times 1$ .
C) $A B$ is $3 \times 3$ ; $B A$ is $3 \times 3$ .
D) $A B$ is $1 \times 1$ ; $B A$ is $3 \times 3$ .