Exercise · ZW-IDENTITY-ELEMENT-010 · ★★★ Advanced
In (ℤ,·), is 0 an identity?
Choose one option.
Show answer
- A. No, because 0·a=0 and not always a
Explanation
In (ℤ,·), 0 is not an identity: 0 · a = 0, which is not a unless a = 0. The identity of multiplication is 1.
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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