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.

Question

Let ∗ be a binary operation on the set Q of rational numbers as follows: a ∗ b = ab 2 Find which of the binary operations are commutative and which are associative.

Philoid · Accepted Answer

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.

Let ∗ be a binary operation on the set Q of rational numbers as follows:a ∗ b = ab2Find which of the binary operations are commutative and which are associative.

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.