A = {1,2,3,4} ,how many commutative binary operation are possible on A with identity element 4 and each element is its own inverse

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A = {1,2,3,4} ,how many commutative binary operation are possible on A with identity element 4 and each element is its own inverse

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Amal A 7th Mar, 2020

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akshatk 15th Nov, 2020

Hi, if you fix 4 as the identity element, then you are free to define the mapping for the pairs (1, 2), (2, 3) and (3, 1) .

Now, every element is its own inverse means that a= a^-1. Now, we also know that a*a^-1=e, where e is the identity element.

Commutative basically means that changing the order of the operands does not change the result, basically meaning a*b= b*a

Now, it is very easy to understand what is going on as all the essential parts have been explained. I hope you will be able to solve from here! If not, you can ask further!

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