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Find order of all the elements of the Group = {1,-1, i, -i}. The binary operator is defined as a b = ab.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Find order of all the elements of the Group =
{1,-1, i, -i}. The binary operator is defined as a b = ab.

Expert Solution

Step 1

The given group is:

G = {1, -1, i, -i}

The binary operation * is defined as a * b = ab.

Clearly 1 is the identity element of the group G; for we see:

a * 1 = 1 * a = a; for all a in G

Step by step

Solved in 2 steps

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