First, note that A [ 1 0 ] {\displaystyle A{\begin{bmatrix}1\\0\end{bmatrix}}} and A [ 0 1 ] {\displaystyle A{\begin{bmatrix}0\\1\end{bmatrix}}} are the first and second columns of A {\displaystyle A} , respectively.
The latter is given, and we notice that A [ 1 0 ] = A ( [ 1 1 ] − [ 0 1 ] ) = A [ 1 1 ] − A [ 0 1 ] = [ 5 4 ] − [ 2 2 ] = [ 3 2 ] , {\displaystyle A{\begin{bmatrix}1\\0\end{bmatrix}}=A\left({\begin{bmatrix}1\\1\end{bmatrix}}-{\begin{bmatrix}0\\1\end{bmatrix}}\right)=A{\begin{bmatrix}1\\1\end{bmatrix}}-A{\begin{bmatrix}0\\1\end{bmatrix}}={\begin{bmatrix}5\\4\end{bmatrix}}-{\begin{bmatrix}2\\2\end{bmatrix}}={\begin{bmatrix}3\\2\end{bmatrix}},} so
