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GATE2017 ME-1: 26

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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 ?

  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.
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