For the binary operation a * b = GCD(a, b) on N, the inverse of element 5 is:
For the binary operation a * b = GCD(a, b) on N, the inverse of element 5 is:
- A. 1/5
- B. 1
- C. 5
- D. Does not exist
Answer: D) Does not exist
Explanation: An identity element e must satisfy GCD(a, e) = a for all a in N. No such natural number e exists. Since there is no identity, inverses cannot exist.
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