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

If `A = [{:(1,2,-1),(-1,1,2),(2,-1,1):}]`, then det (adj (adjA)) is

A

`14^4`

B

`14^3`

C

`14^2`

D

14

Text Solution

Verified by Experts

The correct Answer is:
A
We know that for a square matrix of order n
adj (adjA)`=abs(A)^(n-2)A," if " absA ne 0`.
`rArr "det (adj(adj A))" abs(abs(A)^(n-2)A)`
`rArr "det (adj(adj A)) "(abs(A)^(n-2))^nabsA`
`rArr " det(adj)(adj A))" =abs(A)^(n^2-2n+1)`
Here, n=3 and and `absA=14`.
`:. " det(adj(adj A))"=14^4`
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