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:
- 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