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  text: '[summary: An identity [5xy element] in a set $S$ with a [-3kb binary operation] $*$ is an element $i$ that leaves any element $a \\in S$ unchanged when combined with it in that operation.]\n\nAn identity [5xy element] in a set $S$ with a [-3kb binary operation] $*$ is an element $i$ that leaves any element $a \\in S$ unchanged when combined with it in that operation.\n\nFormally, we can define an element $i$ to be an identity element if the following two statements are true:\n\n1. For all $a \\in S$, $i * a = a$. If only this statement is true then $i$ is said to be a *left identity*.\n2. For all $a \\in S$, $a * i = a$. If only this statement is true then $i$ is said to be a *right identity*.\n\nThe existence of an identity element is a property of many algebraic structures, such as [3gd groups], [3gq rings], and [481 fields].',
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