Solution
= Solution
\b[True.] Distribute the <matrix product> while retaining its order:
$$
A^{-1}(A+B)B^{-1}=A^{-1}AB^{-1}+A^{-1}BB^{-1}=B^{-1}+A^{-1}=A^{-1}+B^{-1}.
$$
Only addition is commuted; no commutation of $A$ and $B$ is assumed.
= Solution
\b[True.] Distribute the <matrix product> while retaining its order:
$$
A^{-1}(A+B)B^{-1}=A^{-1}AB^{-1}+A^{-1}BB^{-1}=B^{-1}+A^{-1}=A^{-1}+B^{-1}.
$$
Only addition is commuted; no commutation of $A$ and $B$ is assumed.