Question

Prove that integers are commutative underaddition and multiplication, not under division and subtraction

Answer 1

commutative property- a+b=b+a

addition

2+5=5+2

7=7

If,

a= -7

b=2

-7+2=2+(-7)

-5= -5

this shows that commutative property holds addition

multiplication

a×b=b×a

-5×2=2×-5

-10=-10

this shows that commutative property holds multiplication

subtraction

a - b = b - a

5 - 2 2 - 5

3 -3

this shows that commutative property is not valid for subtraction

division

a/b= b/ a

12/3= 4

3/12= 1/4

this division is not valid for commutative property