Consider the matrix P = \left[\begin{array}{c}\\\{1\end{array}/{\sqrt{2}} , 0 , {1}/{\sqrt{2}} ; 0 , 1 , 0 ; {−1}/{\sqrt{2}} , 0 , {1}/{\sqrt{2}} ; ]} Which one of the following statements about P is INCORRECT?

Correct Answer is : All eigenvalues of P are real numbers

Determinant of P is equal to 1.

Inverse of P is equal to its transpose

All eigenvalues of P are real numbers

GATE Mechanical Engineering (ME) 2017 Shift 1 Solved Paper

Question : 36 of 65

Marks: +1, -0

Consider the matrix

P = {[\table \;{1}/{{√{2}}} , 0 , \;{1}/{{√{2}}} ; 0 , 1 , 0 ; \;{−1}/{{√{2}}} , 0 , \;{1}/{{√{2}}} ; ]}

Which one of the following statements about P is INCORRECT?

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