Can someone help me on where to begin? What do I know about even ordered groups that could help?(adsbygoogle = window.adsbygoogle || []).push({});

My first idea was to incorporate the fact that for an element to be of order 2, it must be it's own inverse. (This made me think of the identity element- I don't know if that's what the proof is about). Secondly, I thought of using a cayley table for arbitrary operation, and for arbitrary amounts of elements. The only problem there is I didn't know how to fill out the table properly, as there was no operation, and I had no idea how to incorporate the fact that G is even ordered into the table.

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# Prove every even ordered group has an element of order 2

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