Check if $$xρy \iff (x^2-y^2)(x^2y^2 - 1) = 1$$ is an equivalence relation.
I know that for it to be an equivalence relation, a relation must have these properties: reflexivity, symmetry and transitivity.
For reflexivity, I tried proving that the left side equals 1, but I failed.
Can someone help me? I really have no idea how these are done.
Reflexivity
It means that $x \rho x$. That translates to $$\left(x^2 - x^2\right)\left(x^2x^2 - 1\right) = 0 \neq 1$$
So $\rho$ is not an equivalence relation. We don't need to check the other properties.