Field/Basic properties/Rules for sign/Fact/Proof/Exercise

Let ${}K$ be a field and let ${}a,b,c$ be elements from ${}K$. Show that the following rules for sign hold.

1. ${}(-a)b=-ab=a(-b)\,.$

2. ${}(-a)(-b)=ab\,.$

3. ${}a(b-c)=ab-ac\,.$

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