State, with a brief explanation, whether the following propositions are true or false. (a) If A and B are nxn matrices with no zero entries, then AB + Onxn. (b) If A and B are square matrices of the same size, then det(A + B) = det(A)+det(B). = (c) The set {[A] [] [8]} ] 5 -1 is a linearly independent subset of R3. 6 8 0 2 (d) T: R3 R4, defined by T - y y 2 - 2 23 + 1 3y - 2 is a linear transformation. 2 (e) Two different matrices may have the same eigenvalues.