List of top Mathematics Questions on Eigenvalues and Eigenvectors asked in IIT JAM MA

Let \(A\) be a \(3\times 3\) real matrix such that given any column vector \(x\in \mathbb{R}^3\), the column vector \(Ax\) is the reflection of \(x\) about the plane

Let \[ P = \begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{pmatrix} \in M_5(\mathbb{C}). \]
Which of the following statements is/are TRUE?