2 A multiplicative group with identity \(e\) contains distinct elements \(a\) and \(r\), with the properties \(r ^ { 6 } = e\) and \(a r = r ^ { 5 } a\).
- Prove that r ar \(= a\).
- Prove, by induction or otherwise, that \(r ^ { n } a r ^ { n } = a\) for all positive integers \(n\).