Genesis 3:16 and your desire shall be to your husband and he shall rule over you. Note: now based on what some teach which is that Adam was the first man and only man on earth and Eve was the only woman, this applies to Adam and Eve because it was taught that these were the only two on earth, however Eve falls first and she fell first, Adam had authority over her because Adam had not fallen yet, however Adam did fall at some point, therefore both were equal in the fall, Adam lost his authority over Eve because he had fallen as well.
Not more and not less. God gave this punishment, not Paul. Adams role in this has no meaning. He got his own consequences and also we man.