(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Linear algebra

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