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



=Definition of Inverse= Let G be a group with operation $$\ast$$


 * $$ \forall \; g \in G: \exists \; g^{-1} \in G: g \ast g^{-1} = g^{-1} \ast g = e_{G} $$

=Usages=
 * 1) If g is in G, g has an inverse g−1 in G
 * 2) b is the inverse of g on group G if
 * b is in G, and
 * b $$\ast$$ g = g $$\ast$$ b = eG.
 * eG here again means the Identity of group G.
 * 1) If b is the inverse of g on group G, then
 * b is in G, and
 * b $$\ast$$ g = g $$\ast$$ b = eG.

=Notice=
 * 1) G has to be a group