Solve the Problem $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & 1 \end{array} \right]$

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

Correct Answer:

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