Let ∗ be a binary operation on the set Q of rational numbers as follows:
a ∗ b = ab2
Find which of the binary operations are commutative and which are associative.
It is given that ∗ be a binary operation on the set Q of rational numbers is defined as
a ∗ b = ab2
We can see that for 2, 3 ϵ Q
2 * 3 = 2. 32 = 18 and 3 * 2 = 3. 22 = 12
⇒ 2 * 3 ≠ 3 * 2
Therefore, the operation * is not commutative.
Also, We can see that (1 * 2) * 3 ≠ 1 *(2 * 3), where 1,2,3 ϵ Q
Therefore, the operation * is not associative.