Q:

Transitive relations and Subsets

I have a question to prove:
If relations R is transitive, than R^2 is transitive. In the answer the professor says that if R is transitive than:
R^2 is a subset of R (I understand why, this is the definision)
Therefore, R^2*R^2 is a subset of R^2. This is the part I don't understand. Is this like a multipication of two sides in an equation?
Thank you.

A:

You believe that $R^2=R\times R\subseteq R$.  Therefore, $$R^2\times R^2=(R\times R)\times (R\times R)\subseteq R\times R=R^2$$

