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Let A be a square matrix of order n. S...

Let A be a square matrix of order n.
Statement - 1 : `abs(adj(adj A))=absA^(n-1)^2`
Statement -2 : `adj(adj A)=absA^(n-2)A`

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:
A
Statement -1 is ture (see Theorem 8 on page 16.7)
`:. abs(adj(adj A))=abs(absA^(n-2)A)=absA^((n-2)n)absA`
`rArr abs(adj(adjA))=abs A^(n^2-2n+1)=absA^((n-1))^2`
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