Let AAA be a 3×33 \times 33×3 matrix with det(A)=3\det(A) = 3det(A)=3. If B=12A2⋅(AT)−1B = \frac{1}{2} A^2 \cdot (A^T)^{-1}B=21A2⋅(AT)−1, find det(B)\det(B)det(B).
38\frac{3}{8}83
98\frac{9}{8}89
278\frac{27}{8}827
111