Suppose r is a partial order on a and s is a partial order

Question

Suppose R is a partial order on A and S is a partial order on B. Define a relation T on A × B such that (a₁, b₁) T (a₂, b₂) iff a₁ R a₂ and b₁ S b₂. Is T a partial order on A x B? Either provide a proof to show that this is true or provide a counter example to show that this is false.