Two number of different or operational exchanges

A = A^b;
b = a^b;

This allows a two-digit exchange to be achieved without the help of a third variable.

Based on the following properties: Arbitrary variable x and its own XOR or result is 0, that is: x^x = 0 arbitrary variable x and 0 to be different or operation, the result is unchanged, namely: X^0 = x xor or operation of the binding: A^b^c = (a^b) ^c = a^ (b^c) The exchange of the XOR: A^b = b^a

Explain why the above exchange works:

A = A^b
b = a^b--> B = (a^b) ^b = a^ (b^b) = A^0 = A, completes the process of A's value to B.
A = a^b--> a = (a^b) ^a = (b^a) ^a = b^ (a^a) = B^0 = B completes the process of B's value to a.