MathCastle
Groups and FieldsEasyGroups and the Group Axioms

Groups and the Group Axioms · Easy problem

For the candidate operation a∗b=a+ba*b=a+b (ordinary addition) on S={1,−1}S=\{1,-1\}, how many of the four group axioms — closure, associativity, existence of an identity in SS, and existence of inverses in SS — actually hold?