Question:
$A$ and $B$ are square matrices of the same order 3 , such that $A B=2 /$ and $|A|=2$, write the value of $|B|$.
Solution:
Given:
$A$ and $B$ are square matrices of order 3
$|A|=2$
$A B=21$
Now, $A B=2 I \Rightarrow|A B|=|2 I \Rightarrow| A|| B|=| 2 I \mid$
$(\because|A B|=|A| B \mid$, if they are square matrices of same order $) \Rightarrow 2|B|=|2 I|$
$(\because|A|=2) \Rightarrow 2|B|=2^{3}|I|$
$(\because$ Order of $I$ is $3 \times 3) \Rightarrow 2|B|=8 \times 1$
Hence, the value of $|B|$ is 4 .