Consider the matrix \[{\text{P}} = \left[ {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}} \\ 0&1&0 \\ {\frac{{ - 1}}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}} \end{array}} \right]\]
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 eigen values of P are real numbers

Answer: Option D