1. The problem statement, all variables and given/known data Prove that any basis of R^n is an orthonormal basis with respect to some inner product. Is the inner product uniquely determined? 2. Relevant equations I am not sure where to begin. Should I just define an arbitrary basis for a arbitrary R^n? I mean I think I understand the question about the inner product being uniquely determined but I am not sure where to begin. 3. The attempt at a solution See above.