What is the concept behind matrix elementary operation? When we try to find inverse of a matrix using elementary operations we write $$A=A*I$$ If we are going to solve by column elementary operation And $$A=IA$$ if it's row elementary operation
I am not able to understand the concept behind it.
Why only these three elementary transformation exist? And how are these derived?
The key point is that:
right multiplication $Av$ correspond to a columns combination of $A$ by the entry values of v
EG
$A\cdot e_1=A\cdot \begin{bmatrix} 1\\0\\0\\.\\0\end{bmatrix}$= first column of $A$
left multiplication $Av$ correspond to a row combination of $A$ by the entry values of v
EG
$e_1^T\cdot A=[1,0,0,...,0]\cdot A$= first row of $A$