If * be the binary operation on the set Z of all integers defined by a * b (a + 3b²), find 2 * 4

Let be a binary operation on the set Q of all rational numbers given as a * b = (2a - b)² for all a, b ∈ Q. Find 3 * 5 and 5 * 3. Is 3 * 5 = 5 * 3?

Let * be a binary operation on N given by a *b = 1 cm of a and b. Find the value of
20 * 16.

Is * (i) commutative, (ii) associative?

Show that * on Z ⁺ defined by a *b = |a –b| is not a binary operation.

Let * be a binary operation on N, defined by a * b = a^b for all a. b ∈ N.

Show that * is neither commutative nor associative.