Center of a quantum matrix algebra

Question

Let $p \in k^\times$ be a nonroot of unity. It seems to be a well-known fact that the center of the quantum matrix algebra $\mathcal{O}_p(M_n(k))$ is generated by the quantum determinant $D_p$. It is not difficult to check that $D_p$ is indeed central but showing that it generates the whole center seems considerably more difficult. I'm sure this has been proved somewhere but I've been unable to track it down.