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 A & B are square matrices of the same order, by the property of determinants we get
$|A B|=|A| \times|B|$
$|A|=3, A B=I$
$\Rightarrow|A B|=1$
$\Rightarrow|A| \times|B|=1$
$3 \times|B|=1$
$|B|=\frac{1}{3}$