Q:

Nilpotent $4 × 4$ matrix

Find a nilpotent $4 × 4$ matrix with only $-1$ and $3$ as entries.

$\begin{bmatrix}
      -1 & -1 & 3 & 3 \\
    3 & -1 & 3 & -1 \\
    3 & -1 & 3& -1 \\
-1 & -1 & 3 & 3
\end{bmatrix}$ is the matrix I came up with, but I don't think it works. Anyone have a better one?

A:

$$
\left(
\begin{array}{cccc}
3 & 3 & 3 & 3 \\
-1 & -1 & -1 & -1 \\
-1 & -1 & -1 & -1 \\
-1 & -1 & -1 & -1 \\
\end{array}
\right)
$$

