Question
$$\begin{aligned}&\text { If } a \text { and } b \text { are elements in a field, show that } a b=0 \text { if and only if either }\\&a=0 \text { or } b=0\end{aligned}$$
Step 1
First, we need to show that if either $a=0$ or $b=0$, then $ab=0$. This is straightforward since the product of any element with the additive identity (0) is 0 in a field. So, if $a=0$ or $b=0$, then $ab=0$. Show more…
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