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$If P is an orthogonal matrix and Q = P A P^{T} and x = P^{T} Q^{1000} P, then x^{- 1} is, where A is involutary matrix$

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A1000

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Correct option is B

Q=PAPT∴x=PTQ1000Px=PTPAPT1000Px=PTPAPTPAPT999Px=IAPTPAPTPAPT998Px=AIAPTPAPT998Px=A2PTPAPTPAPT997Px=A3PTPAPT997P⋮x=A1000(∵A is involutary )x=I

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If P is an orthogonal matrix and Q=PAPT and x=PTQ1000P, then x−1 is, where A is involutary matrix

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$If P is an orthogonal matrix and Q = P A P^{T} and x = P^{T} Q^{1000} P, then x^{- 1} is, where A is involutary matrix$