If both A−12I 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 BA is skew-symmetric matrix of even order (A′−12I)(A−12I)=I and (A′+12I)(A+12I)=I ⇒A+A′=0 ⇒A′=−A ⇒A2=−34I
or (−34)n=(det(A))2
Hence, n is even.