---
tag: GDBV09GFYB
kind: statement
role: proposition
name: Uniqueness of identity element
sources:
  - wikipedia: en:19447@r1375700306
    locator: Group (mathematics), section Elementary consequences of the group axioms > Uniqueness of identity element
    note: adopted
    mention: wikipedia://en/19447#65QT
    sections: [Statement]
inventory: [GQ4CPSKYED]
---

## Statement

The group axioms imply that the identity element is unique; that is, there exists only one identity element: any two identity elements $e$ and $f$ of a group are equal, because the group axioms imply $e=e\cdot f=f$. It is thus customary to speak of *the* identity element of the group.