State whether the following statements are true or false. Justify.
(i) For an arbitrary binary operation `∗` on a set N, `a ∗ a = a ∀a ∈ N`.
(ii) If `∗` is a commutative binary operation on `N`, then `a ∗ (b ∗ c) = (c ∗ b) ∗ a`

Explanation

To solve the given statements, we will analyze each statement one by one and provide justifications for whether they are true or false.

### Statement (i):
**Statement:** For an arbitrary binary operation `∗` on a set N, `a ∗ a = a ∀a ∈ N`.

**Analysis:**
1. A binary operation is defined as an operation that combines two elements from a set to produce another element from the same set.
2. The statement claims that for any binary operation `∗`, the result of `a ∗ a` should equal `a` for all `a` in the set N.
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