Im trying to solve $Det(S^{-1}AS)$ given that $S$ is invertable. I do know the answer, which is only the determinant of $A$. However, I don't really understand why you can rearrange the determinant product in the following way. Would someone like to explain to me?
$$Det(S^{-1}AS)=Det(S^{-1})Det(A)Det(S) = Det(S^{-1})Det(S)Det(A) = \frac{1}{Det(S)}Det(S)Det(A)$$.
This step does not make sense to me: $Det(S^{-1})Det(A)Det(S) = Det(S^{-1})Det(S)Det(A)$
Would someone like to explain why we are allowed to do this?