Let * be a binary operation on the set Q of rational numbers as f… - Vidyadip

Question

Let $*$ be a binary operation on the set $Q$ of rational numbers as follows:
$a * b = ab^2$

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Answer

$a * b = ab^2$ and $b * a = ba^2 \neq\text{a}*\text{b}$
$\therefore$ operation * is not commutative.
$(a * b) * c = (ab^2) * c = (ab^2)c^2 = ab^2c^2$
And $a * (b * c) = a * (bc^2) = a(bc^2)^2 = ab^2c^4$
Here, $(\text{a}*\text{b})*\text{c}=\text{a}*(\text{b}*\text{c})$
$\therefore$ operation $*$ not is associative.

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