We know :
| Adj(A) | = |A|n-1
Now extending this result we can solve as :
Adj(A) . Adj(Adj(A)) = |Adj(A)| . I where I is identity matrix
==> | Adj(A) . Adj(Adj(A)) | = |Adj(A)|n
==> | Adj(Adj(A)) | = |Adj(A)|n-1 = |A|(n-1)^2
==> | Adj(Adj(A)) * Adj( Adj(Adj(A)))| = | Adj(Adj(A)) |n
==> | Adj( Adj(Adj(A))) | = | Adj(Adj(A)) |n-1
==> | Adj( Adj(Adj(A))) | = | A |(n-1)^3
Now n = 3 here and given |A| = 2
Therefore
| Adj( Adj(Adj(A))) | = 22^3
==> | Adj( Adj(Adj(A))) | = 256
Hence 256 is the correct answer..