for all possible values of a, if a·b/2=a/2, what must b equal?

$$\\$ \frac{ab}{2}=\frac{a}{2}$\\\\ If $a=0$ then b can equal anything \\\\ If $a\ne0$ then\\ $ \frac{b}{2}=\frac{1}{2} $\\ $ b=1$\\\\\\ So if $a=0$ the $b\in R$ and if $a\ne0$ to zero then $b=1$$ $