Matrices/2x2/Determinant 0/No subspace/Exercise

Let ${}D$ be the set of all real ${}2\times 2$-matrices

${\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}},$

which fulfill the condition

${}a_{11}a_{22}-a_{21}a_{12}=0\,.$

Show that ${}D$ is not a linear subspace in the space of all ${}2\times 2$-matrices.

Create a solution