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If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] , ...

If `A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}]` , then the trace of the matrix `Adj(AdjA)` is

A

`adj (adj A)=A`

B

|adj (adj A)|=1

C

|adj A|=1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`:' |A|=|(3,-3,4),(2,-3,4),(0,-1,1)|=3(-3+4)+3(2-0)+4(-2-0)=1`
`:.` adj (adj A)`=|A|^(3-2)A=A` and `|"adj (adj A)"|=|A|=1`
Also,
`|"adj A"|=|A|^(3-1)=|A|^(2)=1^(2)=1`
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