I have this question, where, we are given that $H$ is a subgroup of $G$, and that $|G : H| = 2$. Now we suppose that $a, b \in G$ but $a, b \notin H$. Why is it true that $ab \in H$?
I know that $|G : H| = 2$ implies the number of distinct left cosets is 2. I think I'm supposed to use lagrange's theorem but I don't know how to apply it here. Any idea why the claim is true?