MathCastle
Groups and FieldsMediumGroups and the Group Axioms

Groups and the Group Axioms · Medium problem

On Q∖{−13}\mathbb Q\setminus\{-\tfrac{1}{3}\}, define a∗b=a+b+3aba*b=a+b+3ab. This operation makes a group with identity element 00. Find the inverse of 22 in this group.