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  "body": "\n## Proof\n\n1. Let $a$ be an element of a [[group|G5S1M9]] $G$ with identity $e$. Let $b$ and $c$ both be [[inverses|0BRHKKP333]] of $a$, so $ba = e$ and $ac = e$.\n2. Then $b = be = b(ac)$.\n3. By associativity, $b(ac) = (ba)c$.\n4. Since $ba = e$, $(ba)c = ec = c$.\n5. Thus $b = c$, and $a$ has only one inverse.\n\n## Idea\n\nMultiply one inverse by the element and then by the other inverse. Associativity lets the product collapse in two ways.\n",
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  "name": "Proof of the uniqueness of inverses",
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