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How do we describe all the elements in the cyclic subgroup of GL(2, R) generated by the matrix 1 ? 0 1 [::] 1 1 for n E Z 1 O for n e Z 0 1 A В 0 0 for n e Z for n E Z 0 0

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 18E: Let a and b be elements of a group G. Prove that G is abelian if and only if (ab)2=a2b2.

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Question

How do we describe all the elements in the cyclic
subgroup of GL(2, R) generated by the matrix
1
?
0 1
[::]
1
1
for n E Z
1
O for n e Z
0 1
A
В
[:]
[:]
0 0 for n e Z
for n E Z
0 0
D

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