Slodowy and Nakajima are arguing about the following claim: Any square matrix can be written as a product Ex EP where each Ei is an elementary matrix and P is the matrix for a projection. Slodowy thinks: "The claim is true because elementary matrices are the same as row reduction." Nakajima is not yet convinced: "I see that the determinant of a square matrix is going to be the determinant of such a product, but I don't see why the matrix itself has to be such a product. Explain to Slodowy and Naka jima, using complete sentences, whether or not the claim is true. (i) Fill out the details of Slodowy's argument, or show that the claim is false and explain where Slodowy's argument went wrong. (ii) Fill out the details of Nakajima's observation, or show that it is not true by giving a counterexample