Matrices/2x2/Antideterminant/Multilinear not alternating/Exercise

Let ${}K$ be a field. Show that the mapping

$\operatorname {Mat} _{2}(K)\longrightarrow K,{\begin{pmatrix}a&b\\c&d\end{pmatrix}}\longmapsto ad+cb,$

is multilinear, but not alternating.

Create a solution