How to prove without using of advanced theorems that quaternions algebra $H = \left(\frac{-1,-1}{\mathbb{Z}_p} \right)$, where $p$ is prime that H $\cong\mathrm{Mat}_2({\mathbb{Z}_p})$ My ideas: I tried to build an explicit isomorphism, but as I think it is only possible when $p = 1$ (mod 4), and for $p = 1$ (mod 4) it get it. In my second attempt, I tried to look at them as vector spaces of the same dimension.