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Product of Additive Inverses
gative number multiplied by another negative number results in a positive number. Most of us learnt this rule during our primary or secondary school years.
We want to show that the rule 'negative times negative equals positive' holds, in a general sense, for any set of elements that share certain properties with numbers. In practice, while deciding if some set \( R \) forms a ring, we should always verify that the addition and multiplication operations indeed have \( R \) as the codomain to confirm that the closure property holds. In fact, it holds true in a more general algebraic structure known as a group, which requires only a binary operation with associativity, an identity element, and inverses.
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