The question is: "Prove that it is impossible for a 2x2 matrix to be both nilpotent and idempotent."

I am aware that a nilpotent matrix is where

A^{2}=[0 0]

[0 0]

and a idempotent matrix is where

A^{2}=A

I know it isn't possible, I don't know how to prove it though.

Thanks in advance.