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

Options

A. `12^(4)`
B. `13^(4)`
C. `14^(4)`
D. None of these

Answer

C

Explanation

`|A|=1(1+2)-2(-1-4)-1(1-2)`
`=3+10+1=14`
We know that, adj (adj A) = `|A|.A`
`=14[{:(" "1," "2,-1),(-1, " "1, " "2),(" "2,-1," " 1):}]`
`=[{:(" "14," "28,-14),(-14," "14," "28),(" "28,-14," "14):}]`
det [adj(adj A)] `=|{:(" "14," "28,-14),(-14," "14," "28),(" "28,-14," "14):}|`
`=14^(3)|{:(" "1," "2,-1),(-1," "1," "2),(" "2,-1," "1):}|`
`=14^(3).|A|=14^(3).14=14^(4)`