The binary operation a ∗ b = a² + b² on R has:
The binary operation a ∗ b = a² + b² on R has:
- A. an identity 0
- B. an identity 1
- C. no identity
- D. an identity −1
Answer: C) no identity
Explanation: For e to be identity: a ∗ e = a² + e² = a for all a. This would require e² = a − a², which depends on a. Impossible to have a single e for all a. Hence no identity.
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