Find $A B$ . $A = \left[ \begin{array} { c c }
- 2 & 0 \
0 & 4
\end{array} \right] , B = \left[ \begin{array} { c c }
3 & 0 \
0 & - 2
\end{array} \right]$
A) $$\left[ \begin{array} { l l }
0 & - 6 \
0 & - 8
\end{array} \right]$$
B) $$\left[ \begin{array} { c c }
- 2 & 0 \
0 & 4
\end{array} \right]$$
C) $$\left[ \begin{array} { c c }
- 6 & 0 \
0 & - 8
\end{array} \right]$$
D) $$\left[ \begin{array} { c c }
0 & - 8 \
- 6 & 0
\end{array} \right]$$
E) $$\left[ \begin{array} { l l }
- 6 & 0 \
- 8 & 0
\end{array} \right]$$

Question

Find $A B$ .​ $A = \left[ \begin{array} { c c } 
- 2 & 0 \
0 & 4
\end{array} \right] , B = \left[ \begin{array} { c c } 
3 & 0 \
0 & - 2
\end{array} \right]$ ​
A) $$\left[ \begin{array} { l l } 
0 & - 6 \
0 & - 8
\end{array} \right]$$
B) $$\left[ \begin{array} { c c } 
- 2 & 0 \
0 & 4
\end{array} \right]$$
C) $$\left[ \begin{array} { c c } 
- 6 & 0 \
0 & - 8
\end{array} \right]$$
D) $$\left[ \begin{array} { c c } 
0 & - 8 \
- 6 & 0
\end{array} \right]$$
E) $$\left[ \begin{array} { l l } 
- 6 & 0 \
- 8 & 0
\end{array} \right]$$

Quizplus · Accepted Answer

To find the product $AB$, multiply each element of the rows of $A$ by the corresponding elements of the columns of $B$ and sum them up. The calculation gives $\left[ \begin{array} { c c } -6 & 0 \ 0 & -8 \end{array} \right]$, which matches option C.

Find ABA BAB ​ A=[−2004],B=[300−2]A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 4\end{array} \right] , B = \left[ \begin{array} { c c } 3 & 0 \\0 & - 2\end{array} \right]A=[−20​04​],B=[30​0−2​]

Find $A B$ $A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 4\end{array} \right] , B = \left[ \begin{array} { c c } 3 & 0 \\0 & - 2\end{array} \right]$