Problem10:Which of the following are elementary matrices? 
> (a);
[ 1 0] [ ] [5 1]> (b);
[0 0 1] [ ] [0 1 0] [ ] [1 0 0]> (c);
[2 0 0 2] [ ] [0 1 0 0] [ ] [0 0 1 0] [ ] [0 0 0 1]

Let's call the matrices A, B and C. A is the matrix representation of the elementary row operation that adds (5) times the first equation to the second equation. B is the matrix that performs the swapping between the first and third equations so it is also elementary. Now C is not an elementary matrix. The only way to get a 2 on the upper left corner with an elementary row operation is to multiply the first row of the identity by 2, but then the last column should be 0 and not 2. 