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 $\ast$.