Suppose the matrices $\alpha, \beta$ with the given commutating relations:
$$ \alpha^2=a I\\ \beta^2=b I\\ \alpha\beta=c I\\ \beta\alpha=d I $$
where $a,b,c,d $ are elements of $\mathbb{R}$ and where $I$ is the identity matrix.
How can I find specific examples of $\alpha, \beta$, or even solve for the general case?