Question

Prove Z10= {1,3,7,9} is an abelian group when the binary operation is multiplication modulo 10

Answer 1

Answer:

Step-by-step explanation:

*10 1 3 7 9

1 1 3 7 9

3 3 9 1 7

7 7 1 9 3

9 9 7 3 1

From the table under multiplication modulo 10 it is clear closure, associative properties are satisfied.

When we discuss identity,  “ 1” is the identity element and the inverse of each element is 1*1=1 ;  

3*7 =1 ; 7 * 3 = 1; 9 * 9 = 1  

Ableian commutative property a*b= b*a  :  is also satisfied therefore it is an abelian group

Answer 2

Answer:

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Step-by-step explanation: