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

• A
  $PX =\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$
• B
  $P X=X$
• C
  $P X=2 X$
• D
  $P X=-X$