If A and B are square matrices

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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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