Question

Given a non-empty set \(X\), consider the binary operation \(\ast : P(X) × P(X) \to P(X)\) given by \(A \ast B=A \cap B\; \forall A, \) \( B \;in\; P(X),\) where \(P(X)\) is the power set of \(X\). Show that \(X\) is the identity element for this operation and \(X\) is the only invertible element in \(P(X)\) with respect to the operation \(\ast\).