For the binary operation a ∗ b = a + b − ab on Q, the inverse of an element a (a ≠ 1) is:
For the binary operation a ∗ b = a + b − ab on Q, the inverse of an element a (a ≠ 1) is:
- A. a/(a − 1)
- B. −a/(1 − a)
- C. a/(a + 1)
- D. 1/(a − 1)
Answer: A) a/(a − 1)
Explanation: Identity is 0. Let b be inverse: a ∗ b = 0 → a + b − ab = 0 → b(1 − a) = −a → b = a/(a − 1) (since a ≠ 1).
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