Word Count : 283

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We are given: * $R$ is a commutative ring. * For all $a \in R$, we are told that $a^2 = a$. * We are to show that: $a = -a$, i.e., every element is its own additive inverse. --- ### Step-by-step proof: Given: $$ a^2 = a \quad \text{for all } a \in R. $$ ______ _________ _________ _______ __________ ______ ___.
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