Let AAA be a 3×33 \times 33×3 matrix such that det(A)=3\det(A) = 3det(A)=3. If B=adj(A)B = \text{adj}(A)B=adj(A), where adj(A)\text{adj}(A)adj(A) is the adjugate matrix, find det(B)\det(B)det(B).
999
272727
111
818181