Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Inverse

frame| Inverse: 1. if c is in G, c-1 is in G. 2. c*c-1 = c-1*c = eG Definition of Inverse Let G be a group with operation Usages Usage1If g is in G, g has an inverse g−1 in G Usage2b is the inverse of g on group G if b is in G, and b g = g b = eG. eG here again means the Identity of group G. Usage3If b is the inverse of g on group G, then b is in G, and b g = g b = eG. Notice G has to be a group