Let $X$ be a nonzero $n × n$ matrix such that $X^m = 0$ for some $m ∈ N$. Let $b ∈ N$ be the smallest number for which $X^b = 0$. Show that $b≤ n$.
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$