# Thread: Finite order complex matrix is diagonalizable

1. ## Finite order complex matrix is diagonalizable

how to prove this?

2. Originally Posted by silversand
how to prove this?
If $A^n = I$ then $AA^nA^{-1}$ is a diagnol matrix.

3. Originally Posted by silversand
how to prove this?
Hint: the complex roots of the characteristic equation $x^n=1$ are all distinct.