Solution
= Solution
Writing $\pi=p-qA$ gives $[\pi_x,\pi_y]=iq\hbar B$. Hence $[\rho_x,\rho_y]=i\hbar/(qB)$ and $[R_x,R_y]=-i\hbar/(qB)$ (with signs reversed together if conventions change); all mixed $[R_i,\rho_j]$ vanish.
= Solution
Writing $\pi=p-qA$ gives $[\pi_x,\pi_y]=iq\hbar B$. Hence $[\rho_x,\rho_y]=i\hbar/(qB)$ and $[R_x,R_y]=-i\hbar/(qB)$ (with signs reversed together if conventions change); all mixed $[R_i,\rho_j]$ vanish.