Is there a matrix $A$ such that: $A^4=\begin{pmatrix}0 & 2 & -1 & 1\\ 0 & 0 & 3 &1\\ 0 & 0& 0 & 4\\ 0 & 0 & 0 & 0 \\ \end{pmatrix} ~?$ 
Is there a matrix $A\in \mathbb{C}^{4\times 4}$ such that: $$A^4=\left(\begin{array}{cccc}
0 & 2 & -1 & 1\\
0 &  0 & 3 &1\\
0 & 0& 0 & 4\\
0 & 0 & 0 & 0 \\
\end{array} \right) ~?$$

Any hint is appreciated. Thanks a lot!

If an $n\times n$  matrix satisfies $A^m=0$ for some $m$ then it satisfies $A^n=0$.
notice that if $A^4$ was equal to that matrix then $(A^4)^4=0$, but then $A^4=0$.
