Nilpotent matrix/2/System of equations/Exercise

Let ${}K$ be a field.

a) Characterize the nilpotent ${}2\times 2$-matrices

${\begin{pmatrix}x&y\\z&w\end{pmatrix}}$

over ${}K$ by two equations in the variables ${}x,y,z,w$.

b) Are these equations linear?

Create a solution