Given a non-empty Set X, consider the binary operation * : P(X) x P(X) → P(X) given by A* B = A ∩ B, ∀A, B ∈ P(X), where P(X) is the power set of X. Show that * is commutative and associative and X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation *.
