Let $A, B$ be two diagonalizable matrices of $\mathcal{M}_n(\mathbb{C})$. Show that $A$ and $B$ are similar if and only if they have the same characteristic polynomial.
Let $A, B$ be two diagonalizable matrices of $\mathcal{M}_n(\mathbb{C})$. Show that $A$ and $B$ are similar if and only if they have the same characteristic polynomial.