Product set/Intersection/2/Exercise

Let $M$ and $N$ denote sets, and let $A_{1}, A_{2} \subseteq M$ and $B_{1}, B_{2} \subseteq N$ be subsets. Show the identity

(A_{1} \times B_{1}) \cap (A_{2} \times B_{2}) = (A_{1} \cap A_{2}) \times (B_{1} \cap B_{2}) .