# Group theory - binary operation on G

by Rafael

(Philippines)

**Prove that * is a binary operation on G** • ℚ = set of all RATIONAL NUMBERS

• Set G = ℚ - {1}, set G includes all rational numbers EXCEPT for the number 1.

• Define the operation * as: a*b = a+b-ab

a. Prove that * is a binary operation on G, that is, if a and b are elements of G, then a*b is unique and a*b is an element of G

b. Find the identity element of G?

c. If a is an element of G, find the inverse of a

d. Can we say that (G,*) is a group?

e. If (G,*) defines a group, is it abelian?

f. In G, find x if 3*x*2 =5 and then show that this value of x indeed satisfies this equation.