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?
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Just observe that the quotient by the ideal generated by these elements is at most 1dimensional. 

