If A and B are square matrices of the same order

Question:

If $A$ and $B$ are square matrices of the same order such that $|A|=3$ and $A B=l$, then write the value of $|B|$.

Solution:

Since B are square matrices of the same order, by the property of determinants we get

$|A B|=|A| \times|B|$

$|A|=3, A B=I$

$\Rightarrow|A B|=1$

$\Rightarrow|A| \times|B|=1$

$3 \times|B|=1$

$|B|=\frac{1}{3}$

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