<s>[INST] How to construct a matrix $A$ 
Construct a matrix $A$ such that $A^2\ne 0$ but $A^3=0$.

I need your help to find $A$. Please help. Thanks in advance.
 [/INST] $$\text{Let} \;\;\;A = \begin{pmatrix} 0 & 2 & 0 \\ 0 & 0 & 2 \\ 0 & 0 & 0 \end{pmatrix}$$
$$\text{Then} \;\;\;\; A^2 = \begin{pmatrix} 0 & 0 & 4 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \neq \bf 0$$
$$\text{But} \;\;\;\; \;A^3 = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} = \bf 0$$
</s>