1. The problem statement, all variables and given/known data Let A and B be invertible matrices such that A^-1 + B^-1 is also invertible. Prove that A+B is invertible. 2. Relevant equations A(A^-1) = I B(B^-1) = I (A^-1+B^-1)(A^-1+B^-1)^-1 = I 3. The attempt at a solution I've been trying to manipulate these equations to make something work, but I just can't seem to find the right combination.