Composition of a Realtion with identity is the relation itself

Question

I am completely lost as to how to prove the following, although it appears straightforward. I know how this holds for functions, but how do I prove it specifically for relations? I need to provide a general proof, without taking any specific examples.

This is the question:

Let S be any set, and R be a binary relation on S such that R ⊆ S x S.

Prove that R;I = I;R = R, given that I = {(a,a) | a ∈ S}

Answer 1

xI;Ry iff
exists a with (xIa and aRy) iff
exists a with (x = a and aRy) iff
xRy