Fill in the details of the following argument that
Chapter 8, Problem 8.18(choose chapter or problem)
Fill in the details of the following argument that |AB|=|A||B|. First, if AB is singular, show that at least one of A or B is singular, hence that the determinant of the product and the product of the determinants are both zero. Thus, suppose that AB is nonsingular. Show that A and B can be written as products of elementary matrices, and then show that the determinant of a product of elementary matrices equals the product of the determinants of these matrices.
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