GATE2017 ME-1: 26

Question

Consider the matrix $P=\begin{bmatrix} \dfrac{1}{\sqrt{2}} & 0 &\dfrac{1}{\sqrt{2}} \\ 0 & 1 & 0\\ -\dfrac{1}{\sqrt{2}} &0  & \dfrac{1}{\sqrt{2}}
\end{bmatrix}$ 

Which one of the following statements about $P$ is INCORRECT ?

• A. Determinant of P is equal to $1$.
• B. $P$ is orthogonal.
• C. Inverse of $P$ is equal to its transpose.
• D. All eigenvalues of $P$ are real numbers.