Question:
If $A$ and $B$ are square matrices of order 3 such that $|A|=-1,|B|=3$, then find the value of $|3 A B|$.
Solution:
$|K A|=K^{n}|A|$$[n$ is the order of $A]$
$\Rightarrow|3 A B|=3^{3}|A B| \quad \ldots(1)$
If $A$ and $B$ are square matrices of the same order, then $|A B|=|A||B| .$ So,
$|3 A B|=3^{3}|A||B| \quad$ [From eq. (1)]
$=27 \times-1 \times 3$
$=-81$
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