If A= (1,-1) check whether (A, ×) is not a group
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A= {0,1, -1}
1.clearly A is closed under addition
2.Usual addition is always associative
3. identity element 0\in\:A and satisfies a+0=0+a=a for all a\in\:A
4.
Inverse of 0 is 0
Inverse of 1 is -1
Inverse of -1 is 1
Inverse axiom is true
Hence (A,+) is a Group
1.clearly A is closed under multiplication
2.Usual multiplication is always associative
3. identity element 1\in\:A and satisfies a\times\:1=1\times\:a=a for all [tex]a\in\:A
4.
Inverse axiom is not true because inverse of 0 does not exist
Hence (A,\times) is not a Group
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