An unknown 3x3 matrix A can be identified with the ero1, ero2, ero3, ero4. By following the order of operations below, it can be transformed into an identitymatrix:
$ ero_1: \mathbf{r}_1 + \mathbf{r}_2 \rightarrow \mathbf{r}_2 \\ ero_2: -\frac{1}{5}\mathbf{r}_3 \rightarrow \mathbf{r}_3 \\ ero_3: \mathbf{r}_1 \leftrightarrow \mathbf{r}_3 \\ ero_4: 10\mathbf{r}_3 + \mathbf{r}_1 \rightarrow \mathbf{r}_1 $
Why is one of the matrixproducts $\mathbf{A}\mathbf{E}_4\mathbf{E}_3\mathbf{E}_2\mathbf{E}_1, \mathbf{A}\mathbf{E}_1\mathbf{E}_2\mathbf{E}_3\mathbf{E}_4, \mathbf{E}_1\mathbf{E}_2\mathbf{E}_3\mathbf{E}_4\mathbf{A} $, $\mathbf{E}_4\mathbf{E}_3\mathbf{E}_2\mathbf{E}_1\mathbf{A} $ the identity matrix?
I'm unsure how to identify it as I don't know A. I believe the question is related to the fact that $AB \neq BA$ when it comes to matrices but I can't calculate it.
Guide:
After you perform the first row operation, the matrix becomes $E_1A$.
Write down what happens after the second, third and fourth.