On a set $\{1,2,3,\ldots,12\}$ it is given a relation
$a\rho b\Leftrightarrow MOD(ab,a+b+1)=3.$
Is $\rho$ reflexive (R), symmetric (S) and transitive (T)? Is $\rho^2$ R, S and T?
I know how to check is $\rho$ R, S and T. $\rho$ is not R because, for example, $1\not\rho1.$ $\rho$ is S and $\rho$ is not T ($2\rho 6$ and $6\rho 8$ but $2\not\rho 8$).
Is there any rule for $\rho^2$ to check if it is R, S and T, and more generally for $\rho^n$?