Prove the identity element is unique for groups Prove the id

Solution

Th:In a group G,identity element is unique.

Proof. If possible,let  e_1,e₂ be two identity elements in the group (G,o).

   e₁e₂ = e₂e₁ = e₂ if e₁ is identity in G.

e₂e₁ = e₁e₂ = e₁ if e₂ is identity in G.

Therefore, e₁ = e_2.