Question

If $B$ is a non-singular matrix and $A$ is a square matrix then $det\left(B^{-1}AB\right)$ is equal to

• A. $det\left(A\right)$
• B. $det\left(B\right)$
• C. $det\left(B^{-1}\right)$
• D. $det\left(A^{-1}\right)$

Answer 1

The correct option is A $det\left(A\right)$

$det\left(B^{-1}AB\right)=?$

Where $A$ is a square matrix.

and $B$ is non-singular matrix, so $B$ is invertible and a square matrix.

$det\left(B^{-1}AB\right)$

$=det\left(B^{-1}BA\right)$

$=det\left(I_{n}A\right)$ ( where $I_n$ is an identity matrix of order $n$ )

$=det\left(A\right)$