Inverse of Product

Also known as
When first introducing this concept in a course on group theory, some tutors refer to this theorem as the Socks-Shoes Property.

If one thinks of $a$ as putting on socks, $b$ as putting on shoes, $a^{-1}$ as taking off socks, and $b^{-1}$ as taking off shoes, the theorem demonstrates the order in which one must perform these actions. $a b$ would represent putting on socks followed by shoes. In order to take them off, they must be removed in reverse order, that is, $b^{-1} a^{-1}$.

Less informally it is known as the reversal rule (for group inverses).

Also see

 * Inverse of Commuting Pair