Help me understand more the example of the book so I may understand the whole thing. I am more on detailed-solution-kind of student to make myself get the idea. I am new to this topic and I find Abstract Algebra very difficult to understand and our professor doesn't help me understand but lead me to confusion. That's why I am trying my self to understand all the topics with the help of others who are passionate to this course.
Example 1.2.24 Let ℝ* be the set of all real number except 0. Define * by letting a * b = |a| b
a.)Show that * gives and associative binary operation on ℝ*.
Answer: |ab|c = |ab|c so it is associative.
b.)Show that there is a left identity for * and a right inverse for each element in ℝ*
Answer: Left identity element is 1 and the right inverse is 1/|a|.
c.)Is ℝ* with this binary operation a group?
Answer: It is not a group because both 1/2 and and -1/2 are right inverse of 2.