Exercise · ZW-IDENTITY-ELEMENT-004 · ★☆☆ Basic
What is the neutral element of (ℚ∖{0}, ·)?
Choose one option.
Show answer
- C. 1
Explanation
In (ℚ∖{0}, ·) the operation is multiplication and the neutral element is 1, because 1 · q = q. 0 is outside the set and would not be a multiplicative neutral element.
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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- ZW-IDENTITY-ELEMENT-009 Which expression describes an identity e?