Find the Matrix Product When Possible $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$

Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 0 & - 1 & 0 \\ - 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

A)
$\mathrm{AB}=\left[\begin{array}{crl}0 & 2 & 1 \\0 & -1 & -1 \\0 & 2 & 1\end{array}\right] ; \mathrm{BA}=\left[\begin{array}{rrr}0 & 1 & 0 \\-1 & 0 & 0 \\2 & -2 & 0\end{array}\right]$

B)
$$\mathrm { AB } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\0 & - 1 & 0 \\1 & 0 & 0\end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\0 & - 1 & 0 \\1 & 0 & 0\end{array} \right]$$
C)
$$\mathrm { AB } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\- 1 & 2 & 0 \\2 & - 2 & 0\end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c } 0 & 0 & - 1 \\0 & 1 & 1 \\0 & 0 & - 1\end{array} \right]$$

D)

$$A B = \left[ \begin{array} { r r r } 0 & 1 & 0 \\- 1 & 0 & 0 \\2 & - 2 & 0\end{array} \right] ; B A = \left[ \begin{array} { c r l } 0 & 2 & 1 \\0 & - 1 & - 1 \\0 & 2 & 1\end{array} \right]$$

Correct Answer:

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