|
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
|