Exercise · ZW-INVERSE-ELEMENT-007 · ★★☆ Intermediate
Which statement correctly describes the inverse of an element of a group?
Choose one option.
Show answer
- B. It is unique
Explanation
In a group, the inverse of an element is unique. It is not always the identity (only the inverse of the identity itself is) nor a subset, but an element.
Review the concept: Inverse element
Given \(a\in G\), an element \(b\in G\) is an inverse of \(a\) if operating in both orders gives the neutral element.
\[a\ast a^{-1}=a^{-1}\ast a=e\]
More practice problems: inverse element
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