(i) Zn has element { 0 , 1 , 2 , . . . , n-1 }
We can prove that this set is Group under the Modulo Arithmatic
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(ii) Zn* has element { 1 , 2 , 3 , 4 , … , n-1 }
For this :
(1) closure property satisfied because after doing multiplication we do modulo operation so at last we fall in one of the element from the set
(2) Multiplication with modulo is associative
(3) identity element is 1
(4) Inverse : This is interesting case => There is theorem that says that Multiplicative inverse exist for element iff element is relative prime to the n (here n is Zn )
and we are given n is prime so for any element a ,GCD(n,a) = 1 so for any element in our set we have multiplicative inverse
So inverse exist for every element
So (ii) is also group
Option A is correct