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Identity in Binary Operation

Let * be the ...

Question

Let $$ be the binary operation on N given by $a b = L C M$ of a and b.
(i)Is $*$ commutative?

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Solution

The binary operation $$ on N is defined as $a b = L C M$ of a and b.
It is known that
LCM of a and b =LCM of b and a for $a, b \in N .$
Therefore, $a * b = b * a$ . Thus, the operation $*$ is commutative.

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