a - うん、佐藤さんも入らない？
b - うん、佐藤さんも入ろうか。
I wanted to know why 'a' is correct and 'b' is incorrect. The woman is saying "so you entered a tennis club, is it interesting?" Then the guy answers "sure why don't you enter also with me", so that's why I thought 'b' would be correct, why is 'b' incorrect and 'a' correct?