Can someone help me on where to begin? What do I know about even ordered groups that could help? 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.