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Exercise 4.2.3. Let H be the set - {(; ?) H = : х,у € R (1) Show H- {0}is a group under matrix multiplication (here by 0, we mean the 2 x 2 matrix with all entries 0). (2) Show o : C* → (H – {0},·) is an isomorphism where o is defined by -y P(x+yi)

Exercise 4.2.3. Let H be the set - {(; ?) H = : х,у € R (1) Show H- {0}is a group under matrix multiplication (here by 0, we mean the 2 x 2 matrix with all entries 0). (2) Show o : C* → (H – {0},·) is an isomorphism where o is defined by -y P(x+yi)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.4: Cyclic Groups
Problem 19E
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Exercise 4.2.3. Let H be the set -{; ?) eR}. x -y Н :x,y E (1) Show H – {0} is a group under matrix multiplication (here by 0, we mean the 2 x 2 matrix with all entries 0). (2) Show o : C× → o is defined by (H – {0},·) is an isomorphism where x -y p(x+yi) = (,
Transcribed Image Text:Exercise 4.2.3. Let H be the set -{; ?) eR}. x -y Н :x,y E (1) Show H – {0} is a group under matrix multiplication (here by 0, we mean the 2 x 2 matrix with all entries 0). (2) Show o : C× → o is defined by (H – {0},·) is an isomorphism where x -y p(x+yi) = (,
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