If x and y are elements in a group G and if x⁵ = y³ = e, where e is the identity of G, then the inverse of x²yx⁴y² must be
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Correct answer: B. yxy²x³
Explanation
(x²yx⁴y²)⁻¹ = y⁻²x⁻⁴y⁻¹x⁻². Since x⁵ = e and y³ = e: y⁻² = y, x⁻⁴ = x, y⁻¹ = y², x⁻² = x³. So the inverse is y·x·y²·x³ = yxy²x³.More Discrete Structures and Optimization questions
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