Indicate whether the statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample.
(a) If det(A) = 0, then A is not expressible as a product of elementary matrices.
(b) If the reduced row-echelon form of A has a row of zeros, then det(A) = 0.
(c) The determinant of a matrix is unchanged if the columns are written in reverse order.
(d) There is no square matrix A such that det(AAT) = - 1.