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If A, B and \(\left(adj\left({\mathrm{A}}^{-1}\right)+adj\left({\mathrm{B}}^{-1}\right)\right)\) are non-singular matric…

Q1

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

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

d

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

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