For any X, Y and Z belonging to A, there are (x * y) * z = x * z = x, and x * (y * z) = x * y = x, so (x*y)*z=x*(y*z), and the combination holds. (A，*)

(2)(A, *) is not a commutative semigroup.

The number of elements of is greater than 1. We take two elements of A, X and Y, X is not equal to Y, and x*y = x, y * X = Y, so x*y is not equal to y * X and cannot be exchanged. (a, *) is not a commutative semigroup.

(3)(A, *) has no unit element.

If X is a unit element, then for any x*y=y and x*y=x, y=x, and all elements are unit elements X, which contradicts that the number of elements of A is greater than 1.