Question

If \( G^{*} \) is a group and the order of an element \( a \in G \) is 10, then the order of the inverse of \( a \) is

• A. 10
• B. \( \frac{1}{10} \)
• C. 5
• D. 1

Hint:

The order of an element in a group is the same as the order of its inverse.

Answer 1

The Correct Option is A

Step 1: Properties of group elements.
In a group, the order of an element is the same as the order of its inverse. Therefore, the order of the inverse of \( a \) is also 10.

Step 2: Conclusion.
Thus, the correct answer is option (A).

Final Answer: \[ \boxed{\text{(A) 10}} \]