2. Let G be a group. Prove that the identity element e is unique. Prove that for-1 with aaa € G, there exists a unique inverse element a= e = a ¹a.3. Let GL2 (R) be the group of invertible 2 x 2 matrices over R.(45)(a) Show that A =(b) Compute A-¹.is in GL₂ (R).

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Answered: 2. Let & be a group. Prove that the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 31E: Exercises 31. Let be a group with its center: . Prove that if is the only element of order in ,...

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2. Let & be a group. Prove that the identity element e is unique. Prove that for a € G, there exists a unique inverse element a¹ with aa-¹ = e = a ¹a. 3. Let GL2 (R) be the group of invertible 2 x 2 matrices over R. (45) (a) Show that A = (b) Compute A-¹. is in GL₂ (R).