1. The problem statement, all variables and given/known data Let (R,+,*) be a commutative ring with identity. Show that (R,+) is a group but (R,*) is never a group. 3. The attempt at a solution This question confuses me because I thought a group was defined for a set with a binary operation, i.e. a set that uses multiplication. Also, does binary operation imply multiplication and addition are defined?