Determinant/Bilinear form/Not symmetric/Exercise

Show that the determinant in dimension two, that is, the mapping

$K^{2}\times K^{2}\longrightarrow K,({\begin{pmatrix}x_{1}\\y_{1}\end{pmatrix}},{\begin{pmatrix}x_{2}\\y_{2}\end{pmatrix}})\longmapsto x_{1}y_{2}-x_{2}y_{1},$

is a bilinear form, which is not symmetric.

Create a solution