Question
Thu January 31, 2013 By: Manoj

Let A={1,-1,i,-i} be the set of four 4th roots of unity. Prepare the composition table for multiplication on A and show that multiplication is associative on A

Expert Reply
Wed February 06, 2013

x

1

-1

i

-i

1

1

-1

i

-i

-1

-1

1

-i

i

i

i

-i

-1

1

-i

-i

i

1

-1

 

For associativity:

(1 x 1) x I = 1 x i = i

1 x (1 x i) = 1 x i = i

This way you can show this property for every element of set A.

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