I have been working with the following question for quite awhile: Show that a permutation with an odd order must be an even permutation. I have made some progress, but I am having trouble putting it altogether to make my proof coherent. This is what i have so far: Let e= epsilon Say BA^(2ka+1)= ae. Then BA^(2ka)=BA^(-1). But BA^(2k)=(BA^ka)^2 is even. I know that I am on the right track but I can't seem to put it altogether. Can someone help me please. If I could just have it explained Iam sure I will understand.