Operation 
Commutative 
True / False 
Addition 
a + b = b + a 
True 
Subtraction 
a − b = b − a 
False 
Multiplication 
a × b = b × a 
True 
Division 
a/b=b/a 
False 
So commutativity is always possible for addition &
multiplication, but not for subtraction & division.
For Integers
Let us take two integers 2 & 3
Operation 
Number 
Remark 
Addition 
a + b = b + a Take a = 2 & b = 3
L.H.S a + b = 2 + 3 = 5
R.H.S b + a = 3 + 2 = 5
∴ a + b = b + a 
Since a + b = b + a, ∴ Addition is commutative. 
Subtraction

a − b = b − a Take a = 2 & b = 3
L.H.S a − b = 2 − 3 = −1
R.H.S b – a = 3 − 2 = 1

Since a − b ≠ b − a,
∴ Subtraction is

Multiplication

a × b = b × a Take a = 2 & b = 3
L.H.S a × b = 2 × 3 = 6
R.H.S b × a = 3 × 2 = 6
∴ a × b = b × a

Since, a × b = b × a ∴ Multiplication is commutative. 
Division

a/b=b/a Take a = 2, b = 3
L.H.S a/b = 2/3
R.H.S b/a = 3/2
∴ a/b≠b/a 
Since a/b≠b/a
∴ Division is
