Question

to prove that multiplication of integer is commutative 10 pairs

Answer 1

Let

x=[[a,b]]

x=[[a,b]]

and

y=[[c,d]]

y=[[c,d]]

for some

x,y∈Z

x,y∈Z

.


Then:

x×y

x×y

=

=

[[a,b]]×[[c,d]]

[[a,b]]×[[c,d]]

=

=

[[ac+bd,ad+bc]]

[[ac+bd,ad+bc]]

Definition ofInteger Multiplication

=

=

[[ca+db,da+cb]]

[[ca+db,da+cb]]

Natural Number Multiplication is Commutative

=

=

[[ca+db,cb+da]]

[[ca+db,cb+da]]

Natural Number Addition is Commutative

=

=

[[c,d]]×[[a,b]]

[[c,d]]×[[a,b]]

Definition ofInteger Multiplication

=

=

y×x

y×x

hope it helps u
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