Find the product, AB, if possible.
-$$\mathrm { A } = \left[ \begin{array} { r r }
- 2 & 3 \
3 & 2
\end{array} \right] , \mathrm { B } = \left[ \begin{array} { l l }
- 2 & 0 \
- 1 & 3
\end{array} \right]$$
A) $\left[ \begin{array} { r r } 4 & 0 \ - 3 & 6 \end{array} \right]$

B) $\left[ \begin{array} { r r } 1 & 9 \ - 8 & 6 \end{array} \right]$

C) $\left[ \begin{array} { r r } 9 & 1 \ 6 & - 8 \end{array} \right]$

D) $\left[ \begin{array} { r r } 4 & - 6 \ - 4 & 3 \end{array} \right]$

Question

Find the product, AB, if possible.
-$$\mathrm { A } = \left[ \begin{array} { r r } 
- 2 & 3 \
3 & 2
\end{array} \right] , \mathrm { B } = \left[ \begin{array} { l l } 
- 2 & 0 \
- 1 & 3
\end{array} \right]$$
A) $\left[ \begin{array} { r r } 4 & 0 \ - 3 & 6 \end{array} \right]$

B) $\left[ \begin{array} { r r } 1 & 9 \ - 8 & 6 \end{array} \right]$

C) $\left[ \begin{array} { r r } 9 & 1 \ 6 & - 8 \end{array} \right]$

D) $\left[ \begin{array} { r r } 4 & - 6 \ - 4 & 3 \end{array} \right]$

Quizplus · Accepted Answer

To find the product $AB$, we multiply matrix $A$ by matrix $B$. The product is calculated as follows:$$AB = \left[ \begin{array} { r r } - 2 & 3 \3 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \- 1 & 3\end{array} \right] = \left[ \begin{array} { r r } (-2)(-2) + 3(-1) & (-2)(0) + 3(3) \3(-2) + 2(-1) & 3(0) + 2(3)\end{array} \right] = \left[ \begin{array} { r r } 4 - 3 & 0 + 9 \-6 - 2 & 0 + 6\end{array} \right] = \left[ \begin{array} { r r } 1 & 9 \-8 & 6\end{array} \right]$$

Find the Product, AB, If Possible A) [40−36]\left[ \begin{array} { r r } 4 & 0 \\ - 3 & 6 \end{array} \right][4−3​06​]

Find the Product, AB, If Possible A) $\left[ \begin{array} { r r } 4 & 0 \\ - 3 & 6 \end{array} \right]$