LET G= R\{-1}. Define * on G by a*b = a + ab+b. Find the solution the solution equation 3* x * 2=23  a.0       c.1/3 b.1        d. -1/3 2.)Let G = R\{-1}. Define * on G by a*b= a+ab+b. If 0 is the identity element of G, What is the inverse of a? a. –a           c. a over a+1 b. 1/a         d. –a over a+1 3.)Let be a group and let a,b,c, E G which of the following does not always hold a. a*b=a*c implies b=c b. (a*b)^-1 =a^-1 *b^-1 c. the linear equation y * a=b has unique solution y in G d. The identity element and inverse of each elements are unique

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1.) LET G= R\{-1}. Define * on G by a*b = a + ab+b. Find the solution the solution equation 3* x * 2=23
 a.0       c.1/3
b.1        d. -1/3

2.)Let G = R\{-1}. Define * on G by a*b= a+ab+b. If 0 is the identity element of G,
What is the inverse of a?
a. –a           c. a over a+1
b. 1/a         d. –a over a+1

3.)Let <G,*> be a group and let a,b,c, E G which of the following does not always hold
a. a*b=a*c implies b=c
b. (a*b)^-1 =a^-1 *b^-1
c. the linear equation y * a=b has unique solution y in G
d. The identity element and inverse of each elements are unique

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