True or false? (a) The transpose of a column vector is a row vector. (b) The matrix product bc of a row vector b with n elements times a column vector c with n elements is a scalar. (c) The diagonal elements of a Hermitian matrix must be real numbers. (d) The eigenvalues of a diagonal matrix are equal to the diagonal elements. (e) For a square matrix all of whose elements below the principal diagonal are zero, the eigenvalues are equal to the diagonal elements. (See Prob. 8.20.) (f) Every nonzero column vector with n elements is an eigenvector of the unit matrix of order n. (g) every nonzero linear combination of two eigenvectors that correspond to the same eigenvalue of a matrix is an eigenvector of that matrix. (h) Zero is not allowed as an eigenvalue of a matrix. (i) A zero column vector is not allowed as an eigenvector of a matrix. (j) Every square matrix has an inverse. (k) If AB = AC, then the matrices B and C must be equal. (l) If A is a square matrix of order n and c is a column vector with n elements, then Ac is a column vector with n elements. (m) Every real symmetric matrix is a Hermitian matrix. (n) The sum of the eigenvalues of a square matrix always equals the trace of the matrix.