1. The problem statement, all variables and given/known data Suppose T is a linear operator on a finite dimensional vector space V, such that every subspace of V with dimension dim V-1 is invariant under T. Prove that T is a scalar multiple of the identity operator. 3. The attempt at a solution I'm thinking of starting by letting U and W be subspaces of V with dim U = dim W = dim V-1 This means that U and W are invariant under T. Good start? Where do i go from there to show that T is a scalar multiple of the identity operator?