$\text{ Let }P\text{ be a matrix satisfying }P\left[\begin{array}{c}2\\ -3\end{array}\right]=\left[\begin{array}{c}-11\\ -6\end{array}\right]\text{ and }{P}^2\left[\begin{array}{c}2\\ -3\end{array}\right]=\left[\begin{array}{c}-7\\ -12\end{array}\right]\text{ , then which of the }$following is/are INCORRECT? 

$\text{ Sum of all elements of }\mathrm{P}=5$

$\text{P}\left[{ }_3^2\right]=\left[{ }_6^7\right]$

P is a nil-potent matrix.

$\text{ Let }{a}_{ij}\text{ denote the elements of matrix }\mathrm{P}\text{ . Then, }{a}_{11}\times a_{22}=-2$