JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002Let AAA be a 3×33 \times 33×3 matrix such that ∣adj(adj(adjA))∣=81|\operatorname{adj} (\operatorname{adj}(\operatorname{adj} A))| = 81∣adj(adj(adjA))∣=81. If S={n∈Z:∣adj(adjA)∣(n−1)22=∣A∣3n2−5n−4},S = \left\{ n \in \mathbb{Z} : |\operatorname{adj}(\operatorname{adj} A)|^{\frac{(n-1)^2}{2}} = |A|^{3n^2 - 5n - 4} \right\},S={n∈Z:∣adj(adjA)∣2(n−1)2=∣A∣3n2−5n−4}, then ∑n∈S∣An2+n∣\sum_{n \in S} \left| A^{n^2 + n} \right|∑n∈SAn2+n is equal to:AOption A. 866BOption B. 750COption C. 820DOption D. 732CheckSkip · show solution
