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2014-10-31T10:52:01+05:30

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A ∈ G. Let there be an identity element e in G. 

Then a * e = a    or     a * a⁻¹ = a⁻¹ * a = e,
             where a⁻¹ ∈ A and is called the inverse of a.

For every element a⁻¹ ∈ G,  (a⁻¹)⁻¹ = a ∈ G    since  (a⁻¹) * (a⁻¹)⁻¹ = a⁻¹ * a = e

Thus if  < a > = G , then  < a⁻¹ > = G

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