If the binary operation ∗ on R − {−1} is defined by a ∗ b = a + b + ab, then the inverse of 2 is:

If the binary operation ∗ on R − {−1} is defined by a ∗ b = a + b + ab, then the inverse of 2 is:

• A. 1/3
• B. −2/3
• C. −1/3
• D. 2/3

Answer: B) −2/3

Explanation: Identity e: a ∗ e = a + e + ae = a → e(1+a) = 0 → e = 0. Inverse of a: a ∗ b = 0 → a + b + ab = 0 → b(1+a) = −a → b = −a/(1+a). For a = 2, inverse = −2/(1+2) = −2/3.