Prove rules 3 through 6 of Theorem 12.1.
REFERENCe:
Theorem 12.1 Rules of Multiplication
Let a, b, and c belong to a ring R. Then
1. a 0 = 0a = 0.
2. a (–b) = (–a)b = –(ab).
3. (–a)(–b) = ab.†
4. a ( b – c) = ab – ac and (b – c)a = ba – ca.
Furthermore, if R has a unity element 1 , then
5. (–1)a = –a.
6. (–1)(–1) = 1.
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