To show that \( G \) is Abelian, we need to demonstrate that \( G \) is a **commutative group**, meaning that for any two elements \( a \) and \( b \) in \( G \), the operation in the group satisfies \( a \cdot b = b \cdot a \).

However, the current question doesn't specify what group \( G \) refers to or its operation. Usually, these types of problems follow from group properties or specific definitions of the group \( G \).

Could you clarify or provide more context about the group \( G \)? It could be, for example:
- A group of matrices,
- A group of permutations,
- A group of real or complex numbers under a certain operation, etc.

Let me know if you can give more detail, and I'd be happy to proceed further!

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Would you like additional context on Abelian groups, or do you have other questions? Here are some related topics:

1. What is a group in abstract algebra?
2. What is a commutative operation?
3. Why is the property of being Abelian important?
4. Can all groups be Abelian?
5. Examples of non-Abelian groups.

**Tip:** In Abelian groups, the order in which you combine two elements doesn't matter, but this isn't true for all groups.

This solution demonstrates how to prove that a group G is Abelian, using fundamental concepts of abstract algebra and group theory. The problem requires understanding the commutative property in groups and the definition of Abelian groups, suitable for undergraduate-level abstract algebra students.

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