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If nth-order square matrix A is a orthog...

If nth-order square matrix A is a orthogonal, then `|"adj (adj A)"|` is

A

Statement -1 is True, Statement -2 is true, Statement -2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement -2 is True, Statement -2 is not a correct explanation for Statement -1.

C

Statement -1 is True, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

Verified by Experts

The correct Answer is:
C
We have known that `abs (adj(adjA))=absA^((n-1)^2)`.
So, statement -2 is false.
If A is an orthogonal matrix, then`absA=pm1`
`:. Abs(adj(adjA))=absA^((n-1)^2)=(pm1)^((n-1)^2)=pm1`.
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