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