Solution
= Solution
Use the multiplicativity rule for the <cobraided bialgebra> and $\Delta b=a\otimes b+b\otimes d$:
$$
r(a^2,b)=r(a,b_{(1)})r(a,b_{(2)})
=r(a,a)r(a,b)+r(a,b)r(a,d).
$$
The generator table has $r(a,b)=0$, so
$$
\boxed{r(a^2\otimes b)=0.}
$$
Here the tensor notation means the value of the scalar form on the two displayed arguments, not multiplication within $M_q(2)$.