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CSS Pure Mathematics QUESTION #4086
Question 1
In the group \((Q^+, *)\) where \(a * b = \dfrac{ab}{2}\), what is the inverse of element \(a\)?
  • \(\dfrac{1}{a}\)
  • \(\dfrac{2}{a}\)
  • \(\dfrac{4}{a}\)✔️
  • \(\dfrac{a}{2}\)
Correct Answer Explanation
For inverse \(a'\): \(a * a' = e = 2 \Rightarrow \dfrac{a \cdot a'}{2} = 2 \Rightarrow a' = \dfrac{4}{a}\). Verify: \(a * \dfrac{4}{a} = \dfrac{a \cdot (4/a)}{2} = \dfrac{4}{2} = 2 = e\) ✓.