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

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

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