If A and B are square matrices

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, $|3 A B|=\underline{675}$.

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