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 = ab²

✓

Answer

a * b = ab² and b * a = ba² $\neq\text{a}*\text{b}$
$\therefore$ operation * is not commutative.
(a * b) * c = (ab²) * c = (ab²)c² = ab²c²
And a * (b * c) = a * (bc²) = a(bc²)² = ab²c⁴
Here, $(\text{a}*\text{b})*\text{c}=\text{a}*(\text{b}*\text{c})$
$\therefore$ operation * not is associative.

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