6. Consider the set Zn under the operation of multiplication. (a) Build a Cayley table for n = 5 and for n = 6 (b) Describe with as much detail as possible any similarities or differences in the two tables. In particular i. Is there an element that behaves like an identity and if so what is it? Is it unique? Why or why not? ii. Does every element have an inverse? Which do and what are their inverses and which do not? (c) Does there appear to be any relationship between the value n and the elements that have inverses? (d) What, if anything, can be said about the set Zn\[0] for n = 5? What about for n = 6?

6. Consider the set Zn under the operation of multiplication. (a) Build a Cayley table for n = 5 and for n = 6 (b) Describe with as much detail as possible any similarities or differences in the two tables. In particular i. Is there an element that behaves like an identity and if so what is it? Is it unique? Why or why not? ii. Does every element have an inverse? Which do and what are their inverses and which do not? (c) Does there appear to be any relationship between the value n and the elements that have inverses? (d) What, if anything, can be said about the set Zn\[0] for n = 5? What about for n = 6?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.1: Sets

Problem 10E

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