证明题：设<G,*>为群,如果任意aG有a*a=e(其中e为G上关于*运算的单位元),试证<G,*>是交换群。

证:由 <img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/152107722952578f2b2afa898471aaf0a75d5f9791ea3image39.png"><img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1521077229610535cb329184d41f8b7cd6a2f5e6e88dcimage40.png">∴&lt;G,*&gt;是交换群
证:由 ∴<G,*>是交换群