9 The binary operation ⊕ acts on the positive integers \(x\) and \(y\) such that
$$x \oplus y = x + y + 8 \quad \left( \bmod k ^ { 2 } - 16 k + 74 \right)$$
where \(k\) is a positive integer.
9
- Show that ⊕ is commutative.
9
- (ii) Determine whether or not ⊕ is associative.
Fully justify your answer.
9 - Find the values of \(k\) for which 3 is an identity element for the set of positive integers under