Let a binary operation ‘*’ be defined on a set A. The operation will be commutative if

The correct option is a*b=b*a.

Step-by-step Explanation:

A binary operation, denoted by $*$, on a non-empty set $A$ is a function that associates any two elements of $A$ to another element in $A$.

By definition, a binary operation $*$ on a set $A$ is said to be commutative if changing the order of the operands does not change the final result. In mathematical terms, for all elements $a$ and $b$ in the set $A$, the operation must satisfy:
$$a*b=b*a$$
Therefore, the relation a*b=b*a defines the commutative property of the binary operation.

To understand the other options:
1. $(a*b)*c=a*(b*c)$ defines the associative property.
2. $(b○c)*a=(b*a)○(c*a)$ represents the distributive property of the operation $*$ over another operation $○$.
3. $a*b=a$ is a specific definition of an operation (often called left projection) and does not represent a general algebraic property like commutativity.