9th Edition

ISBN: 9781305657960

Author: Joseph Gallian

Publisher: Cengage Learning

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Chapter 3, Problem 69E

Let G = G L ( 2 , R ) and H = { [ a 0 0 b ] | a and b are nonzero integers } under the operation of matrix multiplication. Prove ordisprove that H is a subgroup of G L ( 2 , R ) .

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Chapter 3, Problem 68E

Chapter 3, Problem 70E

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Chapter 3 Solutions

Contemporary Abstract Algebra

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Let G = G L ( 2 , R ) and H = { [ a 0 0 b ] | a and b are nonzero integers } under the operation of matrix multiplication. Prove ordisprove that H is a subgroup of G L ( 2 , R ) .

Solution Summary: The author explains that H is a nonempty subgroup of GL(2,R). By the definition of multiplication of matrices, it is easy to see the closure

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Chapter 3 Solutions