Is $\le$ a binary operation? I am a little confused with $\le$. Is it a binary operation?
I know the definition of binary operation that is any function from $A×A \rightarrow A$ and $A$ non empty.
Kindly help me to understand the concept.

A binary operation is, as you said, a function from $A \times A \to A$. An example of this might be $+ : \mathbb{N} \times \mathbb{N} \to \mathbb{N}$. Binary operations are functions - they take in two inputs, and give you an output.
What you are considering is a binary relation, which is a subset $R \subseteq \mathbb{N} \times \mathbb{N}$. Given two elements $m,n \in \mathbb{N}$, we can ask if $(m,n) \in R$. Thus, relations give us a way of answering true/false questions. In your case, $\leq$ takes in two naturals (or objects in $A$), and says "yes" or "no".
So, in $\mathbb{N}$, we might write $\leq \subseteq \mathbb{N} \times \mathbb{N}$ where $(m,n) \in \leq$ if and only if $m$ is actually less than or equal to $n$.

I hope this helps ^_^
