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.

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:

- Commutative property
- Associative property
- Distributive property over another operation defined in the same set of objects
- Existence of an identity element
- Existence of an absorbing element

### 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