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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

always -1 if n is even

B

always 1 if n is odd

C

always 1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since A is orthogonal, we have
`A A^(T)=I`
or `|A A^(T)|=1`
or `|A^(2)|=1`
or `|A|= pm 1`
Now `|"adj. (adj. A)"|=|A|^((n-1)^(2))`
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