Question

show that
(adj B)^-1 = adj(B^-1)

Answer 1

It is well known that B^-1=adj(B)/det(B), so adj(B)=det(B).B^-1. Similarly, adj(B^-1)=det(B^-1).B. Hence adj(B^-1).adj(B)=det(B)det(B^-1).B.B^-1=I.