Proof involving nonsingular matrices. 1. The problem statement, all variables and given/known data If (I + A) is nonsingular, prove that (I - A)(I + A)-1 = (I + A)-1(I - A), and hence (I - A)/(I + A) is defined for the matrix. I've proved it like this: Let (I - A)(I + A)-1 = A, and (I + A)-1(I - A) = B. B-1 = (I - A)-1(I + A) B-1A = I Premultiplying by B, we get A = B. Is this proof correct?