JEE Math Practice Question

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

1. A.820
2. B.866
3. C.750
4. D.732