Question

If $A$ and $B$ are two non singular square matrices of same order, then $|A^{-1}BA|$ is

• A. $0$
• B. $|B|$
• C. $1$
• D. $|A|$

Answer 1

The correct option is B $|B|$

We know that $|PQ|=|P||Q|$
$\Rightarrow |A^{-1}BA|=|A^{-1}||BA|=|A^{-1}||B||A|=|A^{-1}||A||B|=|A^{-1}A||B|=I|B|=|B|$