JEE Main 2025 — Matrices Question with Solution
JEE Main 2025 (7 Apr Shift 1)
Question
Let be a matrix such that
$\begin{aligned}
& |\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))|=81 . \text { If } \\ & \mathrm{S}=\left\{\mathrm{n} \in \mathbb{Z}:(|\operatorname{adj}(\operatorname{adj} A)|)^{\frac{(n-1)^2}{2}}=|A|^{\left(3 n^2-5 n-4\right)}\right\}
\end{aligned}\sum_{n \in S}\left|A^{\left(n^2+n\right)}\right|$ is equal to
$\begin{aligned}
& |\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))|=81 . \text { If } \\ & \mathrm{S}=\left\{\mathrm{n} \in \mathbb{Z}:(|\operatorname{adj}(\operatorname{adj} A)|)^{\frac{(n-1)^2}{2}}=|A|^{\left(3 n^2-5 n-4\right)}\right\}
\end{aligned}\sum_{n \in S}\left|A^{\left(n^2+n\right)}\right|$ is equal to
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Show full solutionCorrect option: D
Correct answer
D732
Step-by-step explanation
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This is a previous-year question from JEE Main 2025, covering the Matrices chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.