Let `A` be a square matrix of order 3 such that
adj. (adj. (adj. A)) `=[(16,0,-24),(0,4,0),(0,12,4)]`. Then find
(i) `|A|` (ii) adj. A

Explanation

We know that adj. (adj. A) `=|A|^(n-2)A`, where n is order of matrix.
`:.` adj. (adj. (adj. A))`=|"adj. A"|^(n-2)` adj. A
`=(|A|^(n-1))^((n-2))` adj. A
For `n=3`,
adj. (adj. (adj. A))`=|A|^(2)` adj. `A=[(16,0,-24),(0,4,0),(0,12,4)]`
`:. |A|^(6)|"adj. A"|=256`
`implies |A|^(6)|A|^(2)=2^(8)`
`implies |A|=2`
`implies` adj. `A=1/4 [(16,0,-24),(0,4,0),(0,12,4)]=[(4,0,-6),(0,1,0),(0,3,1)]`