If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.

HINT: Consider $A = \begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}$

consider $$A=\begin{bmatrix} 2 & 1\\ -4 & -2 \end{bmatrix}$$

Given two nonzero orthogonal vectors $u, v \in \mathbb{R}^n$. Let $A = vu^T$, then

$$ A^2 = vu^Tvu^T = 0 $$