Representation ring of $PSU(3)$

Question

It is known that any irreducible representations of $PSU(3)$ come from irreducible representations $V_{aL_1+bL_2}$ where $a\geq b\geq 0$ and $a+b$ is divisible by 3. Is it true that the representation ring $R(PSU(3))$ is generated by $X=[V_{3L_1}]$, $Y=[V_{2L_1+L_2}]$ and $Z=[V_{3L_1+3L_2}]$? If so is the ring isomorphic to \begin{eqnarray}\mathbb{Z}[X, Y, Z]/(Y^3-Y^2-2Y(X+Z)-XZ-X-Y-Z)\end{eqnarray}