JEE Advanced 2012 Paper 2 Mathematics Q4

Mathematics

Problem

P

is a

3\times3

matrix such that

P^T=2P+I

, where

P^T

is the transpose of

P

and

I

is the

3\times3

identity matrix, then there exists a column matrix

X=\begin{bmatrix}x\\y\\z\end{bmatrix}\ne\begin{bmatrix}0\\0\\0\end{bmatrix}

such that