For the Hopf algebra $SL_q(N)$ it is clear that the kernel of the counit contains the ideal generated by the elements $(u^i_i1)$ and $u^i_j$, for $i \neq j$. However, I cannot seem to arrive at at proof that it is in fact generated by these elements. Does anyone how to do this?
Just observe that the quotient by the ideal generated by these elements is at most 1dimensional. 

