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 $$X = \begin{bmatrix}x \\y \\z\end{bmatrix} \neq \begin{bmatrix}0 \\0 \\0\end{bmatrix}$$ such that

A

$$PX =\begin{bmatrix}0 \\0 \\0\end{bmatrix}$$

B

$$PX = X$$

C

$$PX = 2X$$

D

$$PX = -X$$