For the binary operation a * b = a + b + ab on R − {−1}, the inverse of an element a is:
For the binary operation a * b = a + b + ab on R − {−1}, the inverse of an element a is:
- A. −a
- B. 1/a
- C. −a/(a + 1)
- D. a/(a + 1)
Answer: C) −a/(a + 1)
Explanation: Let x be the inverse of a. Then a * x = 0 (the identity). a + x + ax = 0 → x(1 + a) = −a → x = −a/(a + 1).
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