How to determine the automorphism group of $\mathbb{Z}_p\times \mathbb{Z}_p$ where $p$ is a prime? Or more specifically, how to determine the element of order $2$ in this group?
I got stuck here, since I only know that if two finite groups $H$ and $K$, where $(|H|,|K|)=1$, then $\text{Aut}(H\times K) = \text{Aut}(H) \times \text{Aut}(K)$. But $p$ and $p$ are not relatively prime.
Any hints or solutions are welcomed, thanks!