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

# Definition of Inverse

editLet G be a group with operation

# Usages

edit- If
*g*is in G,*g*has an inverse*g*^{−1}in G *b*is the inverse of*g*on group G if*b*is in G, and*b**g*=*g**b*=*e*_{G}.*e*_{G}here again means the Identity of group G.

- If
*b*is the inverse of*g*on group G, then*b*is in G, and*b**g*=*g**b*=*e*_{G}.

# Notice

edit- G has to be a group