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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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 2000-20 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?
Transcribed Image Text: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 2000-20 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?
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