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SSC Pure Mathematics QUESTION #4085
Question 1
Let \(Q^+\) be the set of positive rationals with operation \(a * b = \dfrac{ab}{2}\). What is the identity element of the group \((Q^+, *)\)?
  • \(1\)
  • \(2\)✔️
  • \(\dfrac{1}{2}\)
  • \(4\)
Correct Answer Explanation
For identity \(e\): \(a * e = a \Rightarrow \dfrac{ae}{2} = a \Rightarrow e = 2\). Verify: \(a * 2 = \dfrac{2a}{2} = a\) ✓. The identity element is \(2\).