Proving the order of quaternion group is 8 Given this relation
$Q_8=\left<i,j\mid ij=j^{-1}i, ji=i^{-1}j\right>$. I want to show $Q_8$ has order $8$.
I first tried to prove $i^4=1$, but I got stuck. Can anyone give me constructive hint or suggestion?

First, show $i^2=j^2$, then look at $i^4=ij^2i$
