Label the following statements as being true or false. (a) If two rows of A are identical, then det(A) = 0. (b) If B is a matrix obtained from A by interchanging two rows, then det(B) = -det(A). (c) If B is a matrix obtained from A by multiplying a row of A by a scalar c, then det(A) = det(B). (d) If B is a matrix obtained from A by adding a scalar multiple of row i to row j (i + j), then det(B) = det(A). (e) If E is an elementary matrix, then det(E) = ±1. (f) If A, Be Mnxn(F), then det(AB) = det(A) • det(B). (g) A matrix M is invertible if and only if det(M) = 0. (h) A matrix M e Mnxn(F) has rank n if and only if det(M) # 0. (i) The determinant of a matrix may be evaluated by expanding along any row or column. () det(4') = -det(A). (k) The determinant of a diagonal matrix is the product of its diagonal entries. (1) Every system of n linear equations in n unknowns can be solved by Cramer's rule. (m) Let AX = B be the matrix form of a system of n linear equations in n unknowns, where X = (x1, x2,...,x„}'. If det(A) # 0 and if M is the matrix obtained from A by replacing the kth row of A by B', then for each k (1 < k < n), Xx = [det(A)]¬1.det(M).