Question

verify that .
[adj A]^-1 =adj (A^-1)

Answer 1

general, A*(adj A)=(det A)I, so A^(-1)=(1/det A)(adj A) if A is invertible. From these, you can see that
A^(-1)*(adj A^(-1) )=det(A^(-1))I, so
(1/det A) (adj A) (adhj A^(-1))=(1/det A) I,so
(adj A)(adj A^(-1))=I, so
adj (A^(-1))=(adj A)^(-1).

Also
A*A^(-1)=I=A^(-1)*A, so
(A^(-1))^(-1)=A whenevery A is invertible.


I suspect that this is simply a situation where you are asked to verify these results for just this one matrix. So, find A^(-1). Then find adj A^(-1). Then find adj A, then find (adj A)^(-1). Compare. Then find (A^(-1))^(-1) and compare to A.