A\left(\begin{array}{c} -1 \\ 0 \end{array}\right) = \left(\begin{array}{c} -a_1 \\ -a_3 \end{array}\right) = 0 \implies a_1 = 0, \quad a_3 = 0 \implies A = \left(\begin{array}{cc} 0 & a_2 \\ 0 & a_4 \end{array}\right) = \\ \\ a_2\left(\begin{array}{cc} 0 & 1 \\ 0 & 0 \end{array}\right) + a_4\left(\begin{array}{cc} 0 & 0 \\ 0 & 1 \end{array}\right)