Inverse of Field Product with Inverse

Theorem
Let $\struct {F, +, \times}$ be a field whose zero is $0$ and whose unity is $1$.

Let $a, b \in F$ such that $a \ne 0$.

Then:
 * $\paren {a \times b^{-1} }^{-1} = b \times a^{-1}$

This can also be expressed using the notation of division as:
 * $1 / \paren {a / b} = b / a$