Let A be a \(3\times 3\) matrix such that \(|adj(adj(adj\mathrm{A}))|=81\). If \(S=\left\{n \in \mathbb{Z}:(|\operatorna…

Let A be a \(3\times 3\) matrix such that \(|adj(adj(adj\mathrm{A}))|=81\). 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 \(\sum _{\mathrm{n}\in \mathrm{S}}\left|{\mathrm{A}}^{\left({\mathrm{n}}^{2}+\mathrm{n}\right)}\right|\) is equal to

[JEE Main 2025, 7 Apr (Shift 1)]