If possible, find AB and state the order of the result. $$A = \left[ \begin{array} { c c c }
5 & 0 & 0 \
0 & 4 & 0 \
0 & 0 & - 3
\end{array} \right] , B = \left[ \begin{array} { c c c }
5 & 0 & 0 \
0 & - 5 & 0 \
0 & 0 & 4
\end{array} \right]$$
A) $\left[ \begin{array} { c c c }
25 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3
B) $\left[ \begin{array} { c c c }
23 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3
C) $\left[ \begin{array} { c c c }
27 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3
D) $\left[ \begin{array} { c c c }
21 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3
E) $\left[ \begin{array} { c c c }
29 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3

Question

If possible, find AB and state the order of the result.   $$A = \left[ \begin{array} { c c c } 
5 & 0 & 0 \
0 & 4 & 0 \
0 & 0 & - 3
\end{array} \right] , B = \left[ \begin{array} { c c c } 
5 & 0 & 0 \
0 & - 5 & 0 \
0 & 0 & 4
\end{array} \right]$$  
A) $\left[ \begin{array} { c c c } 
25 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3 
B) $\left[ \begin{array} { c c c } 
23 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3 
C) $\left[ \begin{array} { c c c } 
27 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3 
D) $\left[ \begin{array} { c c c } 
21 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3 
E) $\left[ \begin{array} { c c c } 
29 & 0 & 0 \
0 & - 20 & 0 \
0 & 0 & - 12
\end{array} \right]$ Order: 3 × 3

Quizplus · Accepted Answer

Multiplying matrices A and B element-wise (since both are diagonal matrices), we get: $5*5=25$, $4*(-5)=-20$, and $(-3)*4=-12$, resulting in a 3x3 matrix.

If Possible, Find AB and State the Order of the Result