# Properties of an Operation

## Properties of an Operation

An operation defined in a set of objects has specific characteristics called properties.
The properties of an operation are very diverse and depend on the type of operation.

Here is a list of the most commonly encountered properties:

### Example

Multiplication in the set of integers is an operation to which the following properties apply:

• Commutative property: the multiplication of integers is a commutative operation:
3 × (-4) = -12 = (-4) × 3
• Associative property: the multiplication of integers is an associative operation:
(3 × (-4)) × 5 = 3 × ((-4) × 5) = -60
• Distributive property: the multiplication of integers is distributed over the addition of integers:
4 × (12 + (-6)) = (4 × 12) + (4 × (-6))  =  48 + (-24) = 24
• Existence of an identity element: the integer 1 is neutral for the multiplication of integers:
25 × 1 = 25 = 1 × 25
• Existence of an absorbing element: the integer 0 is absorbing for the multiplication of integers:
25 × 0 = 0 = 0 × 25