I know I need to use the inverse matrice, but the problem is (the parameter) $k$, because it's a variable that can take any value depending on $k$, but it's not a variable. Think of the derivative $f'(n)(x)$, where $n$ is not a variable. I have no clue on what to do exactly.
$f_k(m,n)^T=(m-kn,n)^T=\begin{pmatrix}1&-k\\0&1\end{pmatrix}\begin{pmatrix}m\\n\end{pmatrix}$
What is $f_k^{-1}$?