Identity : For any literals a we have `a xx 1 = a = 1 xx a`.

Property 7 for any integer a we have a xx(-1)=-a=(-1)xx a

Property 5 (existence of multiplicative identity): for every integer awe have a xx1=a=1xx a the integer 1 is called the multiplicative identity for integers.

Associativity : For any literal a we have a+0=a=0+a Here 0 is known as the additive identity.

Property 2 (commutativity): for any two integers a and bwe have a xx b=b xx a that is multiplication of integers is commutative.

Commutativity : For any two literals a and b we have a+b=b+a

Commutativity : For any two literals a and b we have ab=ba

Property 6 (property of zero): for any integer we have a xx0=0=0xx a

Property 3 (Associativity): the multiplication of integers is associativie.for any three integers abc we have a xx(b xx c)=(a xx b)xx c

Associativity : For any three literals ab and c we have (ab)c=a(bc)

Property 4 (distributivity of multiplication over addition): the multiplication of integers is distributive over their addition.that is for any three integers a bc we have (1) a xx(b+c)=a xx b+a xx c(2)(b+c)xx a=b xx a+c xx a