Really am mixed , I have read a definition of bounded linear operator as it defined below
A bounded linear operator $U: H \to H$ on a Hilbert space $H$ is called a unitary operator if it satisfies $U^{*}U=UU^{*}=I$ , where $U^{*}$ is the adjoint of $U$, $I$ is the identity operator
From that definition we have $ U^{-1}=U^{*}$ , Now my question is : Does $ U^{-1}$ present a compositional inverse of $ U $ or its Multiplicative inverse in Quantum mechanics ?