If $A^m=I$ then A is Diagonalizable
Let $A$ be an $n\times n$ complex matrix. If $A^m=I_n$ for some positive integer $n$. How to show that $A$ is diagonalizable?
Hint
What we can say for the polynomial $x^m-1$?
If $A^m=I$ then A is Diagonalizable
Let $A$ be an $n\times n$ complex matrix. If $A^m=I_n$ for some positive integer $n$. How to show that $A$ is diagonalizable?
Hint
What we can say for the polynomial $x^m-1$?