Question:
If $A$ and $B$ are square matrices of order 3 such that $|A|=-1,|B|=3$, then $|3 A B|=$________
Given:
$A$ and $B$ are square matrices of order 3
$|A|=-1$
$|B|=3$
Solution:
Now,
$|3 A B|=|3 A||B| \quad(\because|A B|=|A||B|$, if they are square matrices of same order $)
$=|3 A| \times 3 \quad(\because|B|=3)$
$=3^{3}|A| \times 3 \quad(\because$ Order of $A$ is $3 \times 3)$
$=81|A|$
$=81 \times(-1) \quad(\because|A|=-1)$
$=-81$
Hence, $|3 A B|=\underline{-81}$.
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