$x R x \Rightarrow x^{2}=x \cdot x$ Hence reflexive
$x R y \Rightarrow x^{2}=x y.$
$\Rightarrow x=y y R x$
$\Rightarrow y^{2}=x y$
$\Rightarrow y=x$ Hence symmetric
$x R y$ and $y R z$
$\Rightarrow x^{2}=x y$
$\Rightarrow x=y .$ Also $y^{2}=y z $
$\Rightarrow y=z$
Since $x=z, x \cdot x=z \cdot x$
$\Rightarrow x^{2}=x z$
$\Rightarrow x R z$. Hence transitive.