I'm self studying Artin and I think I understand how right and left cosets work, but I have a question that involves the right cosets of $S_3$, and I'm confused on how to do it. I have $H = \{1,y\}$ so do I just multiply $1,y,xy$ to the right of $H$? Like same process for left cosets but just multiplying the variables to the right of it instead of left?
But that would give me the same as the left cosets and I know that the left and right cosets of $S_3$ are not the same, but then I don't know how else to proceed.