There are various ways to verify the braid relation for R-matrices. These include: 1. Direct brute force calculation. (This is a formidable task even for the "standard" R-matrix associated to SL(n) and is not realistic for more other choices of R.) 2. Show that the R-matrix is a specialization of a universal R-matrix. (This method was used by Schedler to confirm the GGS conjecture and involved a spectacularly complicated combinatorial argument.) 3. Accept the claim without verification. (As I did for 14 years.) In this talk I will give an comprehensible and elementary direct proof of the braid relation for the standard R-matrix and the Cremmer-Gervais R-matrix. These methods may generalize to give a direct proof of the GGS conjecture.