Similar Diagonal Matrices

by jgens
Tags: diagonal, matrices, similar
 P: 1,622 As part of a larger problem involving classifying intertwining operators of two group representations, I came across the following question: If $X$ is an $n \times n$ diagonal matrix with $n$ distinct non-zero eigenvalues, then exactly which $n \times n$ matrices $A$ satisfy the following equality $AXA^{-1} = X$? Does anyone know the answer to this question? Edit: Nevermind. I found a better way of doing the problem that avoids this sort of argument.