Why we have elementary operations on matrix? I just started with matrices, so this might be the stupidest question I ever asked.

When we had to find the inverse of a matrix $A$, we write $A$ as $A = IA$ then we use elementary operations to convert $A$ on LHS to $I$. 
The elementary operations I have been taught is $R_i \to kR_j$, $R_i \to R_j$ and $R_i \to R_i + kR_j$. 
I want to know why we have only these operations and not something like $R_i \to R_i + 10$ ? 
How did somebody came up this 3 operations ? 
It would be nice if the answers are a little bit beginner friendly because I don't know much about linear algebra.
 A: Computing with matrices is really within the domain of computer-based calculations. From this point of view the elementary operations you describe are the most basic things which can be done with the matrix as it would be stored as a data structure in a computer. 
For instance take $R_j \rightarrow kR_j$. A computer can implement this quickly by pulling the registers being used to store the binary numbers in $R_j$ and performing bitwise operations to multiply them by $k$. Since this is the same process on each register, the computer can do it all in parallel if you program it right. The other two are similar.
From a practical standpoint, that's why the elementary operations are useful.
Now, onto the question of why they are elementary. If $V$ is a finite-dimensional linear space, any linear operator from $V$ to itself (for instance, change of coordinates, scaling, rotation) can be written as a square matrix. Since two square matrices of the same dimension yield a third of the same dimension, this also holds for the set of matrices on $V$ themselves regarded as a vector space. If a matrix is multiplied by another matrix, it can be regarded by taking linear combinations of the rows of the first and reading them into the rows of the result. Your elementary operations are all that is needed to construct any linear combination and read it into any row.

I want to know why we have only these operations and not something like    $R_i→R_i+10$? 

This is a scalar being added to a vector -- you can't do that. 
More generally, the reason these operations yield the matrix $A^{-1}$ is because each of them is an irreducible operation which, performed in the right order, send $A$ to $I$. Each operation has a matrix representation and the product of these operations is again a matrix (of the reasons stated above). This matrix must be the inverse, since multiplying it by $A$ gives the identity. 
A: These operations are called elementary row operation because they are the more simpler three operations  with which  we can construct all the invertible matrices starting from the identity matrix (and that can be represented by a matrix multiplication as you will see later).
