Let A be a 3 × 3 matrix such that | adj ( adj ( adj A ))|=81. If S={n ∈ Z:(| adj ( adj A)|)^(((n-1)^2)/2)=|A|^(3 n^2-5 n-4)}, then Σ_n ∈ S|A^(n^2+n)|…

Let $\displaystyle A$ be a $\displaystyle 3 \times 3$ matrix such that $\displaystyle |\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))|=81$. If $\displaystyle S=\left\{n \in \mathbb{Z}:(|\operatorname{adj}(\operatorname{adj} A)|)^{\frac{(n-1)^2}{2}}=|A|^{\left(3 n^2-5 n-4\right)}\right\}$, then $\displaystyle \sum_{n \in S}\left|A^{\left(n^2+n\right)}\right|$ is equal to