Solution
= Solution
Again take $A=B=I_2$. Their sum is also invertible, but $(A+B)^{-1}=I_2/2$, while $A^{-1}+B^{-1}=2I_2$. Thus <matrix inversion is not additive>, <even> when every inverse in the proposed identity exists.
= Solution
Again take $A=B=I_2$. Their sum is also invertible, but $(A+B)^{-1}=I_2/2$, while $A^{-1}+B^{-1}=2I_2$. Thus <matrix inversion is not additive>, <even> when every inverse in the proposed identity exists.