True or False: If vA is an eigenvector of A with eigenvalue λ, then VA is also an eigenvector of A^2. True or False: If vA is an eigenvector of A with eigenvalue λ and A is invertible, then VA is also an eigenvector of A^j. It is known that the product of the eigenvalues of a square matrix is the determinant of that matrix. True or False: Matrix with a nonzero eigenvalue is always invertible. True or False: If Avx = Avx" = Ad B is another matrix satisfying Bv = λv, then VA is an eigenvector for A + B.