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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 ?

- Determinant of P is equal to $1$.
- $P$ is orthogonal.
- Inverse of $P$ is equal to its transpose.
- All eigenvalues of $P$ are real numbers.