U is T-invariant if and only if orthogonal complement of U is T*-Invariant as told on the topic i need to prove if U is a subspace of V and V is a vector space. T ∈ L(V) which L is the set of all operators. I need to prove the both side of this statement below: U is T invariant iff U is T*- invariant T* is adjoint operator of T and U is orthogonal complement of U