Question

How do I prove the basis S = {A,B,C,D}?

Answer 1

\[A=\left[\begin{matrix}-1 & 1 \\ 0\ & 0\end{matrix}\right]\]
\[B=\left[\begin{matrix} 1& 1 \\ 0 & 0\end{matrix}\right]\]
\[C=\left[\begin{matrix}0 & 0 \\ 1 & 0\end{matrix}\right]\]
\[D=\left[\begin{matrix}0 & 0 \\ 0 & 1\end{matrix}\right]\]