A

cute name for an elementary result in

group theory.

We let a

^{-1} denote the

inverse of an

element a in a

group, ie the the element such that a

^{-1}*a = a*a

^{-1} = e, where e is the

identity element. Then (using the

associative property of the

operation in a group)

(a*b)*(b^{-1}*a^{-1}) = a*(b*b^{-1})*a^{-1} = a*a^{-1} = e

Thus the inverse of a*b is b^{-1}*a^{-1}.

This result is sometimes called the shoes-and-socks theorem because of the following analogy: if you want to undo the act of putting your socks and then your shoes on, you first have to remove your shoes and then take off your socks.