Find $| A B |$ .
$A = \left[ \begin{array} { c c }
- 2 & 0 \
0 & 5
\end{array} \right] , B = \left[ \begin{array} { c c }
4 & 0 \
0 & - 2
\end{array} \right]$
A)80
B)78
C)79
D)82
E)81

Question

Find $| A B |$ . 
 $A = \left[ \begin{array} { c c } 
- 2 & 0 \
0 & 5
\end{array} \right] , B = \left[ \begin{array} { c c } 
4 & 0 \
0 & - 2
\end{array} \right]$  
A)80
B)78
C)79
D)82
E)81

Quizplus · Accepted Answer

The determinant of a matrix product $|AB|$ is equal to the product of the determinants of each matrix, $|A| \cdot |B|$. For matrix $A$, $|A| = (-2) \cdot 5 = -10$. For matrix $B$, $|B| = 4 \cdot (-2) = -8$. Thus, $|AB| = -10 \cdot -8 = 80$.

Find ∣AB∣| A B |∣AB∣ A=[−2005],B=[400−2]A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 4 & 0 \\0 & - 2\end{array} \right]A=[−20​05​],B=[40​0−2​]

Find $| A B |$ $A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 4 & 0 \\0 & - 2\end{array} \right]$