Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r } 1 & - 2 \ 4 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & - 1 \ 5 & 4 \end{array} \right]$, find $A B$ and $B A$.
A)
$\mathrm { AB } = \left[ \begin{array} { r r } - 4 & - 3 \ 21 & 2 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r } - 10 & - 9 \ 15 & 8 \end{array} \right]$
B)
$\mathrm { AB } = \left[ \begin{array} { r r } 0 & 2 \ 20 & 12 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r } 0 & 2 \ 20 & 12 \end{array} \right]$
C)
$\mathrm { AB } = \left[ \begin{array} { r r } 10 & 7 \ - 15 & - 16 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r } 4 & 3 \ - 11 & - 22 \end{array} \right]$
D)
$\mathrm { AB } = \left[ \begin{array} { r r } - 10 & - 9 \ 15 & 8 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r } - 4 & - 3 \ 21 & 2 \end{array} \right]$

Question

Quizplus · Accepted Answer

To find $AB$ and $BA$, we perform matrix multiplication for each pair. For $AB$, we multiply each row of $A$ by each column of $B$ and sum the products. For $BA$, we multiply each row of $B$ by each column of $A$ and sum the products. The calculations show that the matrices in choice D are correct for $AB$ and $BA$, respectively.

Find the Matrix Product When Possible A=[1−243]A = \left[ \begin{array} { r r } 1 & - 2 \\ 4 & 3 \end{array} \right]A=[14​−23​]

Find the Matrix Product When Possible $A = \left[ \begin{array} { r r } 1 & - 2 \\ 4 & 3 \end{array} \right]$