MCQMediumJEE Main 2025 · 23 January, Shift 1Inverse & Adjoint of a Matrix

Mathematics Question from JEE Main 2025 · 23 January, Shift 1

If AA, BB, and (adj⁡(A−1)+adj⁡(B−1))\left( \operatorname{adj}(A^{-1}) + \operatorname{adj}(B^{-1}) \right) are non-singular matrices of the same order, then the inverse of A(adj⁡(A−1)+adj⁡(B−1))−1BA \left( \operatorname{adj}(A^{-1}) + \operatorname{adj}(B^{-1}) \right)^{-1} B is equal to:

  • A

    AB−1+A−1BAB^{-1} + A^{-1}B

  • B

    adj⁡(B−1)+adj⁡(A−1)\operatorname{adj}(B^{-1}) + \operatorname{adj}(A^{-1})

  • C

    1∣A∣∣B∣(adj⁡(B)+adj⁡(A))\frac{1}{|A||B|} \left( \operatorname{adj}(B) + \operatorname{adj}(A) \right)

  • D

    AB−1∣A∣+BA−1∣B∣\frac{AB^{-1}}{|A|} + \frac{BA^{-1}}{|B|}

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