Mathematics - Matrix Question with Solution | TestHub

If $P$ is a $3\times 3$ matrix such that $P^T=2P+I$, where $P^T$ is the transpose of $P$ and $I$ is the $3\times 3$ identity matrix, then there exists a column matrix $X=\left[\begin{array}{l}x\\ y\\ z\end{array}\right]\ne \left[\begin{array}{l}0\\ 0\\ 0\end{array}\right]$ such that