Let A be a non-singular matrix of order 3. If det (3 adj (2 adj (( det A) A)))=3^-13 · 2^-10 and det (3 adj (2 A ))=2^m · 3^n, then |3 m +2 n | is…

Let $\displaystyle A$ be a non-singular matrix of order 3. If $\displaystyle \operatorname{det}(3 \operatorname{adj}(2 \operatorname{adj}((\operatorname{det} A) A)))=3^{-13} \cdot 2^{-10}$ and $\displaystyle \operatorname{det}(3 \operatorname{adj}(2 \mathrm{~A}))=2^{\mathrm{m}} \cdot 3^{\mathrm{n}}$, then $\displaystyle |3 \mathrm{~m}+2 \mathrm{n}|$ is equal to $\displaystyle \_\_\_\_$.