A question about diagonalizable matrices Let $A$ be a square matrix such that $A \ne0$, but $A^k=0$ for some integer $k \gt1$. show that $A$ is not diagonalizable.
Could somebody give me some hints?Many thanks

Suppose it is diagonlisable, then $A = \Lambda D\Lambda^{-1}$, then $D^k = 0$ (why?)
then, given $D$ is diagonal, what is $D$,  so what is $A$?
