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 $p=2$
then we get:
$A^2=AA=\begin{bmatrix}
3&9\\
-1& -3
\end{bmatrix}\begin{bmatrix}
3&9\\
-1& -3
\end{bmatrix}=\begin{bmatrix}
0&0\\
0& 0
\end{bmatrix} =0$
Therefore the given matrix is nilpotent.
