Problem: #29 in Strang Linear Algebra Prove that the identity matrix cannot be the product of 3 row exchanges (or five). It can be the product of 2 exchanges (or 4). Now, to start, we try to count the number of rows that are different from the identity matrix. For the first row exchange, it's 2. Second, it becomes either 0, 3, or 4. Third, it can go to 1,2,3,4,6. Four, 0,1,2,3,4,5,6,8... Is this proof sufficient enough?