3 A multiplicative group contains the distinct elements \(e , x\) and \(y\), where \(e\) is the identity.
- Prove that \(x ^ { - 1 } y ^ { - 1 } = ( y x ) ^ { - 1 }\).
- Given that \(x ^ { n } y ^ { n } = ( x y ) ^ { n }\) for some integer \(n \geqslant 2\), prove that \(x ^ { n - 1 } y ^ { n - 1 } = ( y x ) ^ { n - 1 }\).
- If \(x ^ { n - 1 } y ^ { n - 1 } = ( y x ) ^ { n - 1 }\), does it follow that \(x ^ { n } y ^ { n } = ( x y ) ^ { n }\) ? Give a reason for your answer.