Question:
If \(G\) is an abelian group then for all \(a,b \in G\), \(b^{-1} * a^{-1} * b * a\) is equal to
If \(G\) is an abelian group then for all \(a,b \in G\), \(b^{-1} * a^{-1} * b * a\) is equal to
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In Abelian groups, elements commute: \(a * b = b * a\).
Updated On: Apr 23, 2026
- \(a * b\)
- \(a^{-1} * b^{-1}\)
- \(e\)
- None of these
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Formula / Definition}
\[ \text{Abelian: } a * b = b * a \]
Step 2: Calculation / Simplification}
\(b^{-1} * a^{-1} * b * a = b^{-1} * b * a^{-1} * a\) (by commutativity)
\(= (b^{-1} * b) * (a^{-1} * a) = e * e = e\)
Step 3: Final Answer
\[ e \]
\[ \text{Abelian: } a * b = b * a \]
Step 2: Calculation / Simplification}
\(b^{-1} * a^{-1} * b * a = b^{-1} * b * a^{-1} * a\) (by commutativity)
\(= (b^{-1} * b) * (a^{-1} * a) = e * e = e\)
Step 3: Final Answer
\[ e \]
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