Answer
See below
Work Step by Step
An example of a square matrix $A=\begin{bmatrix}
1 & -1 \\ 1 & -1
\end{bmatrix}$
Obtain: $A=\begin{bmatrix}
1 & -1 \\ 1 & -1
\end{bmatrix}\approx\begin{bmatrix}
1 & -1 \\0 & 0
\end{bmatrix}\\
\rightarrow Rowspace(A)=(1,-1)$
If we let the $Rowspace (A)=(x,y) \rightarrow x=-y$
$A=\begin{bmatrix}
1 & -1\\1 & -1
\end{bmatrix}\approx \begin{bmatrix}
1 & 0 \\ 1 & 0
\end{bmatrix}\\
\rightarrow Colspace(A)=(1,1)$
Let $colspace (A)=(x,y) \rightarrow x=y$
Hence, we can see that row space and column space have no nonzero vectors in common.
