(a) Show that every automorphism $\alpha$ of the dihedral group $D_{6}$ is equal to conjugation by an element of $D_{6}$; that is, there is an $h \in D_{6}$ such that

$$\alpha(g)=h g h^{-1}$$

for all $g \in D_{6}$.

(b) Give an example of a non-abelian group $G$ with an automorphism which is not equal to conjugation by an element of $G$.