# Identity element

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In algebra, an identity element or neutral element with respect to a binary operation is an element which leaves the other operand unchanged, generalising the concept of zero with respect to addition or one with respect to multiplication.

Formally, let ${\displaystyle \star }$ be a binary operation on a set X. An element I of X is an identity for ${\displaystyle \star }$ if

${\displaystyle I\star x=x=x\star I\,}$

holds for all x in X. An identity element, if it exists, is unique.