If G be a cyclic group of prime order p ,prove that non identity element of G is a generator of the group.

Question

If G be a cyclic group of prime order p ,prove that non identity element of G is a generator of the group. Let , a be the generator of the group . Then o(a)=p ==>a^p = e, where e be the identity element . G={a,a^2,a^3,.....,a^p(=e)}.