Show that * on R –{ - 1}, defined by is neither commutative nor associative.

let a = 1,b = 0R - { - 1}

a*b = = 1


And b*a = = 0


Hence * is not commutative.


Let c = 3.


(a*b)*c = 1*c =


a*(b*c) = a* = 1*0 = = 1


Hence * is not associative.


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