Discriminant of $\mathrm{Tr}(xy)$ is $p^2$ in a maximal order of discriminant p in a quaternion algebra

Discriminant of $\mathrm{Tr}(xy)$ is $p^2$ in a maximal order of
discriminant p in a quaternion algebra

I am trying to prove that $\mathrm{Tr}(xy)$ has discriminant $p^2$ in a
maximal order of discriminant $p$ in a quaternion algebra. Does anybody
have any hints to get a handle on this?