On the proof that, if $(xy)^2=(yx)^2$ for all $x$ and $y$ in a group, then $xy^2=y^2x$ for all $x$ and $y$
Let G be a group such that $(xy)^2 = (yx)^2$ for all x, y ∈ G. Show that $xy^2 = y^2x$ for all x, y ∈ G.