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

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Inverse:
1. if c is in G, c-1 is in G.
2. c*c-1 = c-1*c = eG

Definition of Inverse[edit]

Let G be a group with operation

Usages[edit]

  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 g = g b = eG.
    eG here again means the Identity of group G.
  3. If b is the inverse of g on group G, then
    b is in G, and
    b g = g b = eG.

Notice[edit]

  1. G has to be a group