Question:

Could anyone show me how to prove this question? So, I know that the order of every element is the smallest integer n such that $\displaystyle g^n=e$, in this case $\displaystyle (g^2)^n = g^3 = e$. I also know that the order of each element of G are arithmetically related to the order of the group, they divide the order of the group. So the order of an element and the order of the group must both be either odd or even (but I don't know how we can prove that they are related). Any help is really appreciated.