I'm not quite sure what you mean for the first one. For the second I assume you're allowed to use that the invertibility of a matrix is equivalent to invertible determinant. If so, then do the following. Let be an -space. Then, there exists an isomorphism afforded by the choice of the ordered basis . Suppose then that then for every one has that and since is invertible one has that exists. Prove then that . Thus, is surjective and the conclusion follows since