[Math] Prove that $\det( P^{-1} AP) =\det(A)$

Question

Let $A$ be an $n × n$ matrix and let $P$ be an $n × n$ invertible matrix. Prove that $\det( P^{-1} AP) = \det(A)$

Pretty lost on this one, partially because I don't understand the relationship between the determinant of a matrix and the determinant of its inverse. Thanks.

Answer 1

Hint: $\det(AB)=\det(A)\det(B)$. Apply this to $PP^{-1}=I$ and to $P^{-1}AP$