If B is a non-singular matrix and A is a square matrix, then $det (B^{-1}AB)$ is equal to
Answer & explanation
Correct answer: option 3
We have,
$|B^{-1} AB|=|B^{-1}||A||B|$
$⇒|B^{-1} AB|=\frac{1}{|B|}|A||B|$ $\left[∵|B^{-1}|=\frac{1}{|B|}\right]$
$⇒|B^{-1} AB|=|A|$