Let T : V -> V be a linear transformation. Prove that if U, and U2 are T'-invariant subspaces of V, then U1 + U2 and U1 n U2 are T-invariant subspaces of V.Let T: V -> V be an invertible linear transformation on a finite-dimensional vector space V. (a) Prove that if A is an eigenvalue of T', then A-'is an eigenvalue of T-1. (b) Prove that if a subspace U of V is T-invariant (that is, T(U) C U), then T(U) = U