Both $R_1$ and $R_2$ are equivalence relations on the set $A$.($A$ is finite)
Define the binary relation $R$ on $A\times A$as follows.
$$R = \{((a_1, a_2),(b_1, b_2)) | (a_1, b_1) \in R_1,(a_2, b_2) \in R_2\}$$
Prove that $R$ is an equivalence relation.
I know a binary relation including reflexivity, Symmetry Transitivity，and assuming $A=\{a_1,a_2,\ldots,a_n\}$ then $$A \times A=\{(a_1,a_1),(a_1,a_2), \ldots,(a_n,a_n)\}$$
But I have no idea how to prove it.
