Exercise · ZW-INVERSE-ELEMENT-009 · ★★☆ Intermediate
If \(b\) is the inverse of \(a\), which equality always holds?
Choose one option.
Show answer
- D. \(a\ast b=e\)
Explanation
If \(b\) is the inverse of \(a\), then \(a\ast b=e\). The other equalities only hold in particular cases, not in general.
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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