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?

Question

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?

TuteeHUB · Accepted Answer

NA

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Determinant of P is equal to 1.

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P is orthogonal

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Inverse of P is equal to its transpose

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All eigenvalues of P are real numbers

1.	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?
A.	Determinant of P is equal to 1.
B.	P is orthogonal
C.	Inverse of P is equal to its transpose
D.	All eigenvalues of P are real numbers
Answer» E.

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?

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