Help me pleaseeeeeeeeeeeeeee

(i)

2 * 6 = 6

6 * 1 = 1

2 * (1 * 6) = 2 * 6 = 6

6 * (2 * 3) = 6 * 3 = 6

(ii) * is commutative if for any a, b ∈ A, we have a * b = b * a. You can verify this visually by checking for symmetry in the table along the main diagonal (going from top left to bottom right).

* is not commutative because

6 * 1 = 1

while

1 * 6 = 6

(iii) If e is the identity, then for any a ∈ A, we have a * e = e * a = a.

Here, 2 is the identity element because 1 * 2 = 1 and 2 * 1 = 1, and the same is true if we replace 1 with 2, 3, or 6.

(iv) Let a ∈ A. a has an inverse a ⁻¹ if a * a ⁻¹ = a ⁻¹ * a = e.

We know that e = 2, so look for any pairs that map to 2. The table shows that

1 * 3 = 2   and   3 * 1 = 2

2 * 2 = 2

so 1 has an inverse of 3, 3 has an inverse of 1, and 2 has itself as its inverse (which is to be expected for the identity).