When we multiply numbers, we have three possibilities
Examples –
 6 × 3 = 18
 2 × 6 = 12
 If both numbers are negative then also the product is positive.
Examples –
 – 6 × – 3 = +18 and – 3 × – 6 = +18
 – 18 × – 2 = +36 and – 2 × – 18 = +36
Examples –
 (3) × (4) = 12 and 3 × (4) = 12
 (18) × (2) = 36 and 18 × (2) = 36
Properties of Multiplication of Integers
Closure property for multiplication of integers :
We have two integers, then the product is also an integer; that is if a and b are integers then a × b is also an integer.
Examples –
 3 × 6 = 18
 210 × 2 = 420
 8 × 6 = 48

Commutative law for multiplication of integers :
If we change the order of numbers to multiply then also we get same product, that is, a × b = b × a.
Examples –
 3 × 6 = 18 and 6 × 3 = 18
 160 × 3 = 480 and 3 × 160 = 480

Associative law for multiplication of integers :
If we have three integers to multiply, we get the same multiplication if we carry out the second multiplication first or first multiplication first, that is, we have a, b and c integers then
(a × b) × c = a × (b × c)
Examples –
 (5× 3) × 2 = 15 × 2 = 30 and 5× (3 × 2) = 5 × 6 = 30
 (6 × 4) × 3 = 24 × 3 = 72 and
6 × (4 × 3) = 6 × 12 = 72

Distributive law of multiplication over addition :
If we have any three integers a, b and c, we have
a × (b + c) = a × b = a× c
Example –
 We have , and and

Multiplication property of 0 :
If we multiply any integer by 0 or 0 by any integer we get 0, that is,
If we have ‘’ as any integer, then
and
Examples –
 and
 and

Existence of multiplication of identity
:
If we multiply any integer by 1 or 1 by any integer, we get the same integer. That is,
If we have ‘’ as any integer, then
and
Examples –
 and
 and
The integer 1 is the multiplicative identity.