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If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then...

If `A=[[3,-3,4],[2,-3,4],[0,-1,1]]` , then

A

`adj(adjA)=A`

B

`abs(adj(adj(A)))=1`

C

`abs(adj(A))=1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Here, `abs(A) = abs((3, -3, 4),(2, -3, 4),(0, -1, 1))`
`= 3 (-3+4) + 3 (2-0) + 4 (-2+0)= 1 ne 0`
`because adj (adjA) = abs(A)^(3-2) A = A ` ...(i)
and `abs(adj (A) ) = abs(A)^(3-1) = abs(A)^(2) = 1^(2) = 1 `
Also, `abs(adj(adj(A))) = abs(A ) = 1 ` [ from Eq. (i) ]
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