Question:
If $A$ and $B$ are square matrices
of order 3 and $|A|=5,|B|=5$, then $|3 A B|=$________
Solution:
Given:
A and B are square matrices of order 3
|A| = 5
|B| = 5
Now,
$|3 A B|=|3 A||B| \quad(\because|A B|=|A||B|$, if they are square matrices of same order $)$
$=|3 A| \times 5 \quad(\because|B|=5)$
$=3^{3}|A| \times 5 \quad(\because$ Order of $A$ is $3 \times 3)$
$=135|A|$
$=135 \times(5) \quad(\because|A|=5)$
$=675$
Hence, $|3 A B|=\underline{675}$.