Given the alternating and $n$-multilinear transformation $f:(K^n)^n \to K^m$.
Show that $$ f_1,\cdots,f_m: (K^n)^n \to K$$
are determinant functions, where $f_i$ is defined as
$$ f_i := \pi_i \circ f$$
where $\pi_i$ is also defined as
$$ \pi_i : K^m \to K, \begin{pmatrix} \alpha_1 \\ \cdots \\ \alpha_m \end{pmatrix} \mapsto \alpha_i, \forall i \in (1,\cdots,m)$$
I could really use some tips here.