Let ∗ be a binary operation on Q defined by a ∗ b = a + b − ab. The identity element for ∗ is:

Let ∗ be a binary operation on Q defined by a ∗ b = a + b − ab. The identity element for ∗ is:

• A. 1
• B. 0
• C. −1
• D. does not exist

Answer: B) 0

Explanation: Let e be identity. a ∗ e = a + e − ae = a → e(1 − a) = 0 → e = 0 (since this must hold for all a). Check e ∗ a = 0 + a − 0 = a. So identity is 0.