Statement-I: The matrix $\left[\begin{array}{ccc}1& -3& -4\\ -1& 3& 4\\ 1& -3& -4\end{array}\right]$ is a nilpotent matrix

Statement-II : The matrix $\left[\begin{array}{ccc}1& 1& 3\\ 5& 3& 6\\ -2& -1& -3\end{array}\right]$ is an idempotent matrix

Which of the above Statement(s) is true ?

$$\begin{gathered} \mathrm{Let} \mathrm{A}=\left[\begin{array}{ccc}1& -3& -4\\ -1& 3& 4\\ 1& -3& -4\end{array}\right] \\ \mathrm{clearly}, {\mathrm{A}}^2=\mathrm{O} \end{gathered}$$

$\therefore$ A is a nilpojent matrix of index ‘2’

 and Let $\mathrm{B}=\left[\begin{array}{ccc}1& 1& 3\\ 5& 3& 6\\ -2& -1& -3\end{array}\right]$

Clearly, ${\mathrm{B}}^2\ne \mathrm{B}$

$\therefore$ B is not an idempotent matrix.

 $\therefore$ Only I is correct.