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Question

# Statement - 1 : if |A|=±1, then the matrix A is orthogonal matrix.Statement - 2 : If A is orthogonal matrix then if |A|=±1

A
Statement-1 is correct and Statement-2 is correct and Statement-2 is correct explanation of Statement-1
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B
Statement-1 is correct and Statement-2 is correct and Statement-2 is not the correct explanation of Statement-1
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C
Statement-1 is incorrect
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D
Statement-1=2 is incorrect
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Solution

## The correct option is C Statement-1 is incorrectIf A is orthogonal matrix , then AAT=IIf we apply det on both sides , we get |A|2=1⇒|A|=±1Therefore statement 2 is correctIf A is Involuntary matrix , then A=A−1If we apply det , we get |A|2=1⇒|A|=±1Therefore if |A|+± , then matrix A need not be orthogonalTherefore statement 1 is incorrectSo the correct option is C

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