Check if relation $\rho$ defined as $x\rho y \Leftrightarrow (x^2-y^2)(x^2y^2-1)=1$ is equivalence relation on $\mathbb{R}$

Question

Check if relation $\rho$ defined as $x\rho y \Leftrightarrow (x^2-y^2)(x^2y^2-1)=1$ is equivalence relation on $\mathbb{R}$

Relation is not reflexive: $(\forall x \in\mathbb{R})x\rho x \Leftrightarrow (x^2-x^2)(x^4-1)=0\neq 1$

Is this correct?

Answer 1

Yes that is correct given that it is not reflexive.

You should try to see how you could make it an equivalence relation.