If $\mathrm { A } , \mathrm { B }$, 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 $\mathrm { A } \left( \operatorname { adj } \left( \mathrm { A } ^ { - 1 } \right) + \operatorname { adj } \left( \mathrm { B } ^ { - 1 } \right) \right) ^ { - 1 } \mathrm {~B}$, is equal to\\
(1) $\mathrm { AB } ^ { - 1 } + \mathrm { A } ^ { - 1 } \mathrm {~B}$\\
(2) $\operatorname { adj } \left( \mathrm { B } ^ { - 1 } \right) + \operatorname { adj } \left( \mathrm { A } ^ { - 1 } \right)$\\
(3) $\frac { A B ^ { - 1 } } { | A | } + \frac { B A ^ { - 1 } } { | B | }$\\
(4) $\frac { 1 } { | A B | } ( \operatorname { adj } ( B ) + \operatorname { adj } ( A ) )$