Inverse of Product

Also known as
This theorem is also known 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. $ab$ 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).