A matrix A is said to be Nilpotent Matrix if \[A^2=0\]. i.e square of matrix A is null or zero matrix .
For Example. Consider Matrix A= \[ \begin{bmatrix} 1&2 &3 \\ 1 &2 &3 \\ -1 & -2 &-3 \\ \end{bmatrix}\]
\[ A^2=\] \[ \begin{bmatrix} 1&2 &3 \\ 1 &2 &3 \\ -1 & -2 &-3 \\ \end{bmatrix}\begin{bmatrix} 1&2 &3 \\ 1 &2 &3 \\ -1 & -2 &-3 \\ \end{bmatrix}\]=\[ \begin{bmatrix} 0 &0 &0 \\0 & 0 &0 \\0 & 0 &0 \\ \end{bmatrix}\]
