For any group $\displaystyle G$ prove that $\displaystyle I(G)$ is a normal subgroup of $\displaystyle A(G)$.

Where $\displaystyle I(G)$ denotes the group of inner automorphisms and $\displaystyle A(G)$ denotes the group of automorphisms on a group $\displaystyle G$.

Thanks and Regards,

Kalyan.