1. Again, please note the mistake I made in class and on the lecture notes. I am about to correct the notes and reupload them:
2. The inner product on Sym has the very nice property that it is respected by the antipode; that is, . You may find this useful in the last question of the Short Homework. **If** one of you posts a proof of this fact here, then everyone will be allowed to use it in the homework (and will be very thankful to that person for their effort).