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 $|A|$ is calculated as $ad - bc$ for a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$. For matrix $A$, $|A| = (-2)(5) - (0)(0) = -10$. For matrix $B$, $|B| = (4)(-2) - (0)(0) = -8$. The product of the determinants is $|A||B| = (-10)(-8) = 80$.

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