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If A=[(a,0,0),(0,a,0),(0,0,a)],a!=0 then...

If `A=[(a,0,0),(0,a,0),(0,0,a)],a!=0` then | adj A| is equal to

A

`a^27`

B

`a^9`

C

`a^6`

D

`a^2`

Text Solution

Verified by Experts

The correct Answer is:
C
Since A is a diagona matrix. Therefore,
`absA=axxa=a^3`
Also,
`abs(adjA)=abs(A)^(3-1) [:' abs(adjA)=abs(A)^(n-1)]`
`rArr abs(adjA)abs(A)^2=a^6`
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Section I - Solved Mcqs
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