Define identity element for a binary operation defined on a set. - Vidyadip

Question

Define identity element for a binary operation defined on a set.

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Answer

Let S be a non-empty set and * be a binary operation on S.
If there exist an element $\text{e}\in\text{S}$ such that
a * e = e * a = a for all $\text{e}\in\text{S}$
Then e is called the identity element for the binary operation * on S.
'0' is the identity element for '+' on Z
1 is the identity element for '×' on Z.

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