Answer
See below
Work Step by Step
An example of a square matrix $A=\begin{bmatrix}
3 & 3 \\ 4 & 4
\end{bmatrix}$
Obtain: $A=\begin{bmatrix}
3 & 3 \\ 4 & 4
\end{bmatrix} \approx \begin{bmatrix}
3 & 0\\ 4 & 0
\end{bmatrix}\\
\rightarrow Colspace(A)=(3,4)$
Let permute the rows of $A$ we have:
$\begin{bmatrix}
3 & 3 \\ 4 & 4
\end{bmatrix}\approx\begin{bmatrix}
4& 0 \\ 3 & 0
\end{bmatrix}\\
\rightarrow Colspace(A)=(4,3)$
Hence, we can see that each type of elementary row operation applied to a matrix can change the column space of the matrix.
