Exercise · ZW-IDENTITY-ELEMENT-009 · ★★☆ Intermediate
Which expression describes an identity e?
Choose one option.
Show answer
- B. e∗a=a and a∗e=a for all a
Explanation
An identity satisfies e ∗ a = a and a ∗ e = a for all a. e ∗ a = e is not general, and a ∗ a = e speaks of inverses, not of the identity.
Review the concept: Identity element
An element \(e\in G\) is an identity, or neutral element, if it leaves every element of the group unchanged when operating with it.
\[e\ast a=a\ast e=a \quad \forall a\in G\]
More practice problems: identity element
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