Question

set of non zero rational number is an abelian group​

Answer 1

Answer:

From the definition of rational numbers, the structure (Q,+×) is constructed as the field of quotients of the integral domain (Z,+,×) of integers. Hence from Multiplicative Group of Field is Abelian Group, (Q≠0,×) is an abelian group.

Answer 2

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative.

Explanation:

From the definition of rational numbers, the structure (Q,+×) is constructed as the field of quotients of the integral domain (Z,+,×) of integers. Hence from Multiplicative Group of Field is Abelian Group, (Q≠0,×) is an abelian group.