Let A be a 3 \times 3 matrix such that |{\adj}({\adj}({\adj} A))|= 81. If S= \{n \in \mathbb{Z}:(|{\adj}({\adj} A)|)^{\frac{(n-1)^2}{2}}={|A|}^{ (3 n^2-5 n-4) }\}, then \sum_{n \in S}{| A^{ (n^2+n) } |} is equal to [7 Apr 2025 Shift 1]

JEE Main 7 Apr 2025 Shift 1 Paper

Section: Mathematics

Question : 6 of 75

Marks: +1, -0

Let A be a 3×3 matrix such that |adj(adj(adj‌A))|= 81. If S={n∈ℤ:(|adj(adj‌A)|)‌

(n−1)2

=|A|(3n2−5n−4)}, then ∑n∈S|A(n2+n)| is equal to

[7 Apr 2025 Shift 1]

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