linear algebra - Can I get a matrix's inverse from elementary column operations?

In my class we've been talking about elementary row operations of matrices, for example, to get its inverse. I remember the teacher saying, those operations don't work for columns; however, in my book, it says they do work. Can I use them on columns to get to the identity matrix for instance, so that I can, then, get its inverse.

Answer

The Gauss-Jordan method is based on rows operations by

$$A^{-1}\cdot (A|I)=(I|A^{-1})$$

we can also operate by columns operation that is

$$\begin{pmatrix}A\\I\end{pmatrix}A^{-1}=\begin{pmatrix}I\\A^{-1}\end{pmatrix}$$