(a) Show that if \(G\) is an abelian group and \(n\) is an integer, then \((a b)^{n}=\) \(a^{n} b^{n}\) for all \(a,b, \in G\).

(b) Give an example of a group \(G\), an integer \(n\), and elements \(a, b \in G\) such that \((a b)^{n} eq a^{n} b^{n}\).