Commutativity

The idea will be illustrated using addition and multiplication.

$a+b=b+a$

$a*b=b*a$

Can you see that subtraction lack commutativity.

$a-b \neq b-a$

Actually, Subtraction is a good example of anti-commutativity because the following is true:

$a-b = -(b-a)$

Appendix A

Two operators commute if when you switch the order you get the same result:

A = rotate 30 degrees clockwise

B = rotate 20 degrees clockwise

AB = 30 deg cw + 20 deg cw = 50 deg cw

BA = 20 deg cw + 30 deg cw = 50 deg cw