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

Question

Quizplus · Accepted Answer

Matrix multiplication is performed by taking the dot product of the rows of the first matrix with the columns of the second matrix. After calculating $AB$ and $BA$ using this method, option B provides the correct matrices for $AB$ and $BA$.

Solve the Problem A=[0−10011−101]A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & 1 \end{array} \right]A=​00−1​−110​011​​

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