Although this law seems obvious to everything, it is not. In a space without time (within three dimensions), additive commutative law is absolutely right. But once there is a timeline, this law will not stand.
One of the experiments to prove this theory is as follows:
(1) Take a cube object, such as a thick book or a Rubik's cube. Lay it flat on a horizontal platform.
(2) Let the face directly above, the face facing you parallel to the desktop and the face parallel to the desktop on your right be the first, second and third faces. Their opposite faces are four, five and six.
(3) Operation A is defined as turning this cuboid 180 degrees. That is, three or six sides do not move, one four exchanges, and two or five exchanges. Operation b is defined as turning the left face upward.
(4) After executing a+b, the upward side is the sixth side. After b+a is executed, the upward side is the third side. Obviously a+b is not equal to b+a.
In addition, if additive commutative law is used to add up the infinite numbers, the result may be wrong.