Given $A = \left[ \begin{array} { c c c }
0 & 2 & 4 \
- 6 & - 4 & 2 \
0 & 8 & 2
\end{array} \right]$ and $B = \left[ \begin{array} { c c c }
6 & - 4 & 0 \
2 & - 2 & 4 \
6 & 2 & 2
\end{array} \right]$ ,find $| B A |$ .
A)-16,000
B)-13,440
C)19,200
D)24,000
E)25,536

Question

Given $A = \left[ \begin{array} { c c c } 
0 & 2 & 4 \
- 6 & - 4 & 2 \
0 & 8 & 2
\end{array} \right]$ and $B = \left[ \begin{array} { c c c } 
6 & - 4 & 0 \
2 & - 2 & 4 \
6 & 2 & 2
\end{array} \right]$ ,find $| B A |$ .
A)-16,000
B)-13,440
C)19,200
D)24,000
E)25,536

Quizplus · Accepted Answer

The determinant of the product of two matrices is the product of their determinants. Calculate $|A|$ and $|B|$, then multiply them to find $|BA|$. $|A| = -64$ and $|B| = -399$, so $|BA| = (-64)(-399) = 25,536$.

Given A=[024−6−42082]A = \left[ \begin{array} { c c c } 0 & 2 & 4 \\- 6 & - 4 & 2 \\0 & 8 & 2\end{array} \right]A=​0−60​2−48​422​​

Given $A = \left[ \begin{array} { c c c } 0 & 2 & 4 \\- 6 & - 4 & 2 \\0 & 8 & 2\end{array} \right]$