if $a^2=e$ for all elements $a$ in a group $\text{G},$ then $\text{G}$ must be abelian.
If every element other than e had order $2 ,$ it means that for all elements $a, a^2=e$, hence, every element is inverse of itself.
Since every element is inverse of itself, hence, $\text{G}$ is abelian group.
https://youtu.be/27dpPOLS00Q?t=516
