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Question

If both A12I and A+12I are othogonal matrices, then

A
A is orthogonal
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B
A is skew-symmetric matrix of even order
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C
A2=34I
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D
none of these
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Solution

The correct option is B A is skew-symmetric matrix of even order
(A12I)(A12I)=I and (A+12I)(A+12I)=I
A+A=0
A=A
A2=34I
or (34)n=(det(A))2
Hence, n is even.

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