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Let * be a binary operation defined on Q. Find if the followin

Question

Let $$ be a binary operation defined on $Q$ . Find if the following binary operation is associative.
$a b = a b^{2}$ for $a, b \in Q$ .

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Sebastian Discussed

Let

*

be a binary operation defined on

Q

. Find if the following binary operation is associative.

a * b = a b^{2}

for

a, b \in Q

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

For

*

to be associative

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

We have

L H S = (a * b) * c = (a b^{2}) * c = (a b^{2}) c^{2} = a b^{2} c^{2}

R H S = a * (b * c) = a * (b c^{2}) = a (b c^{2})^{2} = a b^{2} c^{4}

Thus

L H S \neq = R H S

Hence

*

is not associative.

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Question Text	Let $$ be a binary operation defined on $Q$ . Find if the following binary operation is associative. $a b = a b^{2}$ for $a, b \in Q$ .
Answer Type	Text solution:1
Upvotes	150