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If \(A, B\) and \(\left(\operatorname{adj}\left(\mathrm{A}^{-1}\right)+\operatorname{adj}\left(\mathrm{B}^{-1}\right)\ri…

Q1

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

[JEE Main 2025, 23 Jan (Shift 1)]

a

\({\mathrm{AB}}^{-1}+{\mathrm{A}}^{-1}\mathrm{B}\)

b

\(adj\left({\mathrm{B}}^{-1}\right)+adj\left({\mathrm{A}}^{-1}\right)\)

c

\(\frac{1}{|A B|}(\operatorname{adj}(B)+\operatorname{adj}(A))\)

d

\(\frac{{\mathrm{AB}}^{-1}}{|\mathrm{A}|}+\frac{{\mathrm{BA}}^{-1}}{|\mathrm{B}|}\)

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