Let $A$ denote a matrix in $\mathcal{M}_n(\mathbb{C})$. Show that a matrix is nilpotent if, and only if, its characteristic polynomial is equal to $X^n$.
Let $A$ denote a matrix in $\mathcal{M}_n(\mathbb{C})$.
Show that a matrix is nilpotent if, and only if, its characteristic polynomial is equal to $X^n$.