Could you tell me how to prove that a group with presentation $\langle x,y \ | \ x^2, y^2 \rangle$ is generated by $2$ elements of order $2$?
I know it's infinite, because we will have infinitely many combinations of this kind : $xyxyxyxyxyx...$,$yxyxyxyx...$ (there will be both forms there, right?) because we don't assume in the presentation that it is abelian. If we did, we would have $xyx^{-1}y^{-1}=1$ there, next to $x^2=y^2=1$, wouldn't we?
However, I don't know how to (formally) prove that this group is generated by two elements of order $2$.
Could you help?
Thank you.