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Question

A square matrix A is skew-symmetric, such that A2+I=O, then

A
A is orthogonal matrix
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B
A is orthogonal matrix of odd order
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C
A is involutory matrix
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D
A is orthogonal matrix of even order
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Solution

The correct option is D A is orthogonal matrix of even order
Given A is skew-symmetric matrix and A2+I=0

i.eA=A

I=A2=(A)A=AA

A is orthogonal

Now AA=In|AA|=1

|A||A|=1(1)n(|A|)2=1
((|A|)=(1)n|A|)

A is an orthogonal matrix of even order.

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