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Matrices and Determinants question

2025 · 23 Jan · Shift 1 · Q44

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JEE Main
Mathematics
Matrices and Determinants
2025 · 23 Jan · Shift 1 · Q44

Matrices and Determinants question

2025 · 23 Jan · Shift 1 · Q44

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

\mathrm{A}, \mathrm{B}, \operatorname{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

A
$\frac{A B^{-1}}{|A|}+\frac{B A^{-1}}{|B|}$
B
$\operatorname{adj}\left(\mathrm{B}^{-1}\right)+\operatorname{adj}\left(\mathrm{A}^{-1}\right)$
C
$\mathrm{AB}^{-1}+\mathrm{A}^{-1} \mathrm{~B}$
D
$\frac{1}{|A B|}(\operatorname{adj}(B)+\operatorname{adj}(A))$

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