Let $H$ be a subgroup of a group $G$. Then prove that $Ha$ or $aH$ is a subgroup of $G$ if and only if $a\in H.$

Question

I have just tried as follows:

Let $Ha$ be a subgroup of a group $G$. Then, $Ha=H$ $\implies ~a\in Ha$. In converse part i need to show that $Ha=H.$ please correct me if i am wrong and i need your help. Thanks in advance

Answer 1

I'm afraid you're not proving anything useful.

Hint: If $Ha$ is a subgroup of $G$, then $e\in Ha$. This should also give an idea for the converse.