MCQMediumJEE Main 2025 · 7 April, Shift 1Inverse & Adjoint of a Matrix

Mathematics Question from JEE Main 2025 · 7 April, Shift 1

Let AA be a 3×33 \times 3 matrix such that ∣adj⁡(adj⁡(adj⁡A))∣=81.\left| \operatorname{adj}(\operatorname{adj}(\operatorname{adj} A)) \right| = 81. If S={n∈Z:∣adj⁡(adj⁡A)∣(n−1)22=∣A∣(3n2−5n−4)},S = \left\{ n \in \mathbb{Z}: \left| \operatorname{adj}(\operatorname{adj} A) \right|^{\frac{(n - 1)^2}{2}} = |A|^{(3n^2 - 5n - 4)} \right\}, then the value of ∑n∈S∣A(n2+n)∣\sum_{n \in S} \left| A^{(n^2 + n)} \right| is:

  • A

    866866

  • B

    750750

  • C

    820820

  • D

    732732

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