Elementary Row Operation/Examples/Arbitrary Operation on Identity 1

Example of Elementary Row Operation
The matrix:
 * $\mathbf A = \begin {pmatrix} 1 & 0 \\ 1 & 1 \end {pmatrix}$

can be obtained from the identity matrix $\mathbf I_2$ by the elementary row operation $e$ defined as:
 * $e := r_2 \to r_1 + r_2$

Then multiplying the matrix:
 * $\mathbf X = \begin {pmatrix} a & b \\ c & d \end {pmatrix}$

on the left by $\mathbf A$ we get:
 * $\begin {pmatrix} a & b \\ a + c & b + d \end {pmatrix}$

which can be obtained by applying that same elementary row operation $e$ on $\mathbf X$.