Exercise 2, Appendix 0

Let $F$ be an alternative A-algebra, in which the relation $2x = 0$ implies $x = 0$. Show that, for all $x, y, z$ in $F$, $x(yz)x = (xy)(zx)$ (Moufang's identity). (In the identity

successively replace $y$ by $xy$ and $z$ by $zx$.)