Determine the orders of the elements of D∞

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.2: The Kernewl And Range Of A Linear Transformation
Problem 64E
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Determine the orders of the elements of D∞

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Step 1

It is known that,

D=a,b|a2=b2=e

also it can be observed that,

D=abka,abk,bak,bakb

Let xD.

If x=abk, k0, then it can be observed that xn=abnke. so x=.

If x=bak, k0, then it can be observed that xn=banke. so x=.

If x=bakb and k is an even number.

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