Let $\mathrm{A}=\left\{\mathrm{a}_{\mathrm{ij}}\right\}$ be a $3 \times 3$ matrix, where $\mathrm{a}_{\mathrm{ij}}=\left\{\begin{array}{cll}(-1)^{\mathrm{j}-\mathrm{i}} & \text { if } & \mathrm{i}<\mathrm{j}, \\ 2 & \text { if } & \mathrm{i}=\mathrm{j}, \\ (-1)^{\mathrm{i}+\mathrm{j}} & \text { if } & \mathrm{i}>\mathrm{j},\end{array}\right.$, hen $\operatorname{det}\left(3 \operatorname{Adj}\left(2 \mathrm{~A}^{-1}\right)\right)$ is equal to