Therefore, this is not possible and the correct answer is no.

[alingy1]

Can I get this matrix
\begin{smallmatrix}
1&1&0\\ 0&0&1\\ 0&0&0
\end{smallmatrix}
from the identidy matrix I3 like this:


\begin{smallmatrix}
1&0&0\\ 0&1&0\\ 0&0&1
\end{smallmatrix}
Add second row to first row.
Then substract second row from itself.
Is the substraction of a row from itself allowed?

 

[STEMucator]

Can I get this matrix
\begin{smallmatrix}
1&1&0\\ 0&0&1\\ 0&0&0
\end{smallmatrix}
from the identidy matrix I3 like this:\begin{smallmatrix}
1&0&0\\ 0&1&0\\ 0&0&1
\end{smallmatrix}
Add second row to first row.
Then substract second row from itself.
Is the substraction of a row from itself allowed?

No, you can only add or subtract linear combinations of other rows that are not the row itself when performing row operations.

 

[LCKurtz]

If subtracting a row from itself was a legitimate row operation, you could row reduce any matrix to a zero matrix. And, presto change-o, every matrix has rank zero.

 

[HallsofIvy]

In fact, it is NOT possible to get
$$\begin{bmatrix}1& 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1\end{bmatrix}$$
from the identity matrix by "row operations".

If it were then by doing the "reverse" row operations to the identity matrix would give the inverse matrix. And this matrix, since it has one row of all 0s, has determinant 0 and is NOT invertible.

(Every row operation has a reverse- the reverse of "multiply row i by a non-zero number" is "divide row i by the number, the reverse of "swap two rows" is itself, and the reverse of "add x (x non zero) times row j to row i" is "subtract 1/x times row j from row i.)