Letter A and B only.......- Show that the set S of all symmetries of an equilateral triangle formа.a group under composition of functions.b.Determine the centralizer C(R30º) of R30º where R30° is an elementcorresponding to a 30° rotational symmetry.с.Determine the centralizer C(M) of M where M is an elementcorresponding to a reflection symmetry.d.Determine the center Z(S) of S.

We will use the basic knowledge of group theory to answer this question. Note that although you have…

Answered: а. Show that the set S of all…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 3AEXP

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а. Show that the set S of all symmetries of an equilateral triangle form a group under composition of functions.