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Question

If P is an orthogonal matrix and Q=PAPT and B=PTQ1000P, then B1 is, where A is involutory matrix,

A
A
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B
A1000
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C
I
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D
None of these
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Solution

The correct option is B I
Given θ=PAPT,B=PTQ1000P and A is inventory matrix is A2=I

B=PTQ1000P=PT(PAPT)1000P

=PT(PAPT)(PAPT)999P

=IAPT(PAPT)999P[PTP=I]

=APT(PAPT)(PAPT)998P

=AIAPT(PAPT)998P

=A2PT(PAPT)998P

=A1000PTP=A1000=I[A2=I]

As A=I,A1=I

Option C is correct

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