Question

In a group \( (G^*) \), the equation \( x * a = b \) has a:

• A. unique solution \( b * a^{-1} \)
• B. unique solution \( a^{-1} * b \)
• C. unique solution \( a^{-1} * b^{-1} \)
• D. many solutions

Hint:

In a group, each equation has a unique solution due to the existence of an inverse for each element.

Answer 1

The Correct Option is A

Step 1: Understand the properties of groups.
In a group, the equation \( x * a = b \) has a unique solution, which is given by \( x = b * a^{-1} \).
Step 2: Conclusion.
Thus, the unique solution is \( b * a^{-1} \).
Final Answer: \[ \boxed{b * a^{-1}} \]