Ribbon Element, Equivalence of Definitions

Question

In their book Quantum Groups Chari and Pressley define the ribbon element of a quasitriangular Hopf Algebra algebra $(H,R)$ as a special element $\nu\in H$ such that

1. $\nu$ is central in $H$
2. $\nu^2=\mu S(\mu)$
3. $S(\nu)=\nu$

4. $\epsilon(\nu)=1$

   where $\mu=m(S\otimes 1)R_{21}$

I'm trying to get from the Chari and Pressley definition to the following $$ \nu=m((1\otimes \mu^{-1})R)=m((1\otimes \mu)R_{21}) $$

Any help would be appreciated