Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2. Then | A^T A ( adj (2 A ))^-1( adj (4 B ))( adj ( AB ))^-1 AA^T | is equal…

Let $\displaystyle A$ and $\displaystyle B$ be two square matrices of order $\displaystyle 3$ such that $\displaystyle |A|=3$ and $\displaystyle |B|=2$. Then $\displaystyle \left|\mathrm{A}^{\mathrm{T}} \mathrm{A}(\operatorname{adj}(2 \mathrm{~A}))^{-1}(\operatorname{adj}(4 \mathrm{~B}))(\operatorname{adj}(\mathrm{AB}))^{-1} \mathrm{AA}^{\mathrm{T}}\right|$ is equal to :