Mathematics · Group Theory
Let (G, ) be a group. Which of the following statements is false?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If a, b ∈ G, then the linear equations a * x = b and y * a = b may have many solutions.✓
- 2For every a ∈ G, there is unique element a-1 such that a-1 * a = a * a-1 = e.
- 3If a, b, c ∈ G, then a * b = a * c ⇒ b = c.
- 4(b * a)-1 = a-1 * b-1
Correct answer
If a, b ∈ G, then the linear equations a * x = b and y * a = b may have many solutions.
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