Y.S.Han Finite fields 3 Properties of Groups The identity element in a group G is unique. Proof:Suppose there are two identity elements e and e'in G. Then e'=e'*e=e. The inverse of a group element is unique. School of Electrical Engineering Intelligentization,Dongguan University of Technology Y. S. Han Finite fields 3 Properties of Groups • The identity element in a group G is unique. Proof: Suppose there are two identity elements e and e ′ in G. Then e ′ = e ′ ∗ e = e. • The inverse of a group element is unique. School of Electrical Engineering & Intelligentization, Dongguan University of Technology