Answer
See answer below
Work Step by Step
To show that the given matrix is nilpotent, we need to find integer number $p$ which satisfies the condition: $A^p=0$
Hence, we will take $p=3$
then we get:
$A^3=AAA=\begin{bmatrix}
0&1&1\\
0& 0 &1\\
0 & 0 & 0
\end{bmatrix}\begin{bmatrix}
0&0&1\\
0& 0 &1\\
0 & 0 & 0
\end{bmatrix}=\begin{bmatrix}
0&1&1\\
0& 0 &1\\
0 & 0 & 0
\end{bmatrix}=0$
Therefore the given matrix is nilpotent.
