Mathematics · 2025
JEE Main · 23 January 2025, Shift 1 · Q5
If A, B, and ( adj ( A^-1)+ adj ( B^-1)) are non-singular matrices of same order, then the inverse of A ( adj ( A^-1)+ adj ( B^-1))^-1 B, is equal to
If $\displaystyle \mathrm{A}, \mathrm{B}$, and $\displaystyle \left(\operatorname{adj}\left(\mathrm{A}^{-1}\right)+\operatorname{adj}\left(\mathrm{B}^{-1}\right)\right)$ are non-singular matrices of same order, then the inverse of $\displaystyle \mathrm{A}\left(\operatorname{adj}\left(\mathrm{A}^{-1}\right)+\operatorname{adj}\left(\mathrm{B}^{-1}\right)\right)^{-1} \mathrm{~B}$, is equal to
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle \frac{1}{|\mathrm{AB}|}(\operatorname{adj}(\mathrm{B})+\operatorname{adj}(\mathrm{A}))$
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JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.