I have a question regarding Cayley tables, specifically using the composition operator for this particular problem.(adsbygoogle = window.adsbygoogle || []).push({});

I had to miss class the other week and was just now sitting down to catch up on my homework for this class when I was hit with the algebraic structures section. They have a Cayley table with the composition operator. It goes like this

o ] a | b | c | d | < row of operation

-----------------------

a ] a | b | c | d |

============

b ] b | a | d | c |

============

c ] c | d | a | b |

============

d ] d | c | b | a |

Hopefully you can decipher that table :P They ask a series of questions for the problem such as, is it an algebraic structure, name the identity element, associative, commutative etc. I can answer all those questions by looking at the table, I just can't figure out how they have c o b = d.

I have studied the definition of composite, looked back at identity functions, even checked out some other cayley tables for other operators. I see the pattern, but I just cant see why they get that pattern. Is there another way to do it? Because I see the ring pattern for the identity function, but why is c o c = a!!!

I'm sure as soon as someone explains it to me I will bang my head, but I can't seem to get it right now :/. I'm a geology major (if that explains my lack of understanding :P - math minor) so go easy on me :)

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# Homework Help: Cayley Tables and algebraic structures

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