Is $R^2 = R$, if the relation R is transitive?

Question

I am new to relations and while learning about their properties, I thought about this. I tried to prove it, but I don't know how. Also I can't think of a counter example.

Let R be a transitive relation, then $R^2 = R$

Or

$R^2 = R$ if and only if R is a transitive relation.

I also looked on the internet, but didn't find anything useful.

P.S. This is my first question and maybe I made some mistakes or broke some rules about it, so be gentle.

EDIT: This is not the same question as Transitivity of a square of a relation, because I asked how to prove or disprove $R^2 = R$ if R is a transitive relation. The other question is about transitivity of a square of a relation and mine is about the connection between square of a relation and transitivity of a relation.

Answer 1

Let $X=\{x,y\}$ with $x\ne y$, and let $R$ be the relation $aRb\iff a=x\land b=y$. $R$ is transitive because $R^2=\emptyset\subseteq R$.