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Let A=N xx N and let* be a binary operat...

Let A=N` xx` N and let* be a binary operation on A defined by (a, b) * (c,d) = (ad + bc, bd), `AA` (a, b), (c,d) `in` N `xx` N. Show that
(i) * is commutative.
(ii) * is associative.
(iii) A has no identity element.

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