Define on S = Q × Q* the operation (a, b) * (x, y) = (ay+ x, by). Recall that Q* = Q\{0}. 1. Explain why S is closed under *. The explanation should be a brief one-liner, 2. Is * commutative? 3. Show that (S,*) is a group.

Define on S = Q × Q* the operation (a, b) * (x, y) = (ay+ x, by). Recall that Q* = Q\{0}. 1. Explain why S is closed under . The explanation should be a brief one-liner, 2. Is commutative? 3. Show that (S,*) is a group.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.2: Cayley’s Theorem

Problem 12E: Find the right regular representation of G as defined Exercise 11 for each of the following groups....

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Define on S = Q × Q* the operation (a, b) * (x, y) = (ay+ x, by). Recall that Q* = Q\{0}.
1. Explain why S is closed under *. The explanation should be a brief one-liner,
2. Is * commutative?
3. Show that (S,*) is a group.

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