Let AAA be a n×nn \times nn×n matrix. If adj(A)\text{adj}(A)adj(A) is the adjugate matrix and det(A)=k≠0\det(A) = k \neq 0det(A)=k=0, what is det(adj(adj(A)))\det(\text{adj}(\text{adj}(A)))det(adj(adj(A)))?
k(n−1)2k^{(n-1)^2}k(n−1)2
kn2−2n+1k^{n^2-2n+1}kn2−2n+1
kn−1k^{n-1}kn−1
knk^nkn