Consider the matrix \(P = \left[ {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}}\\ 0&1&0\\ {\frac{{ - 1}}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}} \end{array}} \right]\)
Which one of the following statements about P is INCORRECT?
1
Determinant of P is equal to 1.
2
P is orthogonal
3
Inverse of P is equal to its transpose
4
All eigenvalues of P are real numbers