Binary relation of composite function

Question

Suppose S is a binary relation on a set X. If S ◦ S is reflexive, Is S is reflexive? can we prove this with example too and by definition "Let U be a non-empty set and let R be a binary relation on R is reflexive if ∀x ∈ U, (x, x) ∈ R.

Answer 1

There is atleast one case where it does not hold.

Consider $S = \{(a,b),(b,a)\}$

Then $S \circ S = \{(a,a),(b,b)\}$ i.e reflexive even though $S$ is not

Answer 2

Well you could check if S is an equivalence relation or if there is some "partial order relation" on S, because this would then imply that S is reflexive by definition.