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

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

                         $=\det \left(B^{-1}\right).\det B.\det A=\frac{1}{det\left(B\right)}\det \left(B\right).\det A$

                         $=1.\det A=\det A$