Prove that $\operatorname{Null}(A) = \operatorname{Null}(A^T)$ when $A = A^2$ So I first let x belong to $\operatorname{Null}(A) $ i.e $Ax = 0$. Now I tried using the fact that if the length of $A^Tx = 0$ then $A^Tx = 0$.
But I don't know how to prove that $x^TA^TAx = 0$.
Any help will be appreciated.

Consider
$A=\pmatrix{1 & 1\\0 & 0}$ and $x=\pmatrix{1\\-1}$. Are you sure you have the question correctly posted? Am I not understanding something correctly?
