Prove that if $\displaystyle a,b \in \mathbb{F} $, where $\displaystyle \mathbb{F} $ is a field, then $\displaystyle (-a)b = -(ab) = a(-b) $.

This is the same as $\displaystyle -1 \times (a \times b )= (-1 \times a ) \times b = a \times (-1 \times b) $ by associative law?