Matrices/2x2/Column determinant/Multilinear?/Exercise

Let ${}K$ be a field. Is the mapping

$\operatorname {Mat} _{2}(K)\longrightarrow K,{\begin{pmatrix}a&b\\c&d\end{pmatrix}}\longmapsto ac-bd,$

multilinear in den rows? In the columns?

Create a solution