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

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

$\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right),$

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