Order relationships?

Question

Discrete Math

Hello, is "=" a partial order relation?
For example, there is a set A = {1, 2}. Then the Cartesian product A x A = { (1; 1), (2; 2), (1; 2), (2; 1) }.
Hence R = { (1; 1), (2; 2) }, with R = "=".
Then it turns out that R is a partial order relation, since it is reflexive, antisymmetric and transitive. But R is not a linear order relation. After all, ∃ a, b ∈ A !(=>) aRb v bRa.
As I understand it, partial order does not require that each element of the set be in pairs with other elements of the set. Based on this, can we call the set A - partially ordered? After all, a partial order relation is given on the set R.