Question

If $A=\left[\begin{array}{cc}3& 4\\ -5& 7\end{array}\right]$, then $A^2+A$ is _______

Answer 1

$A^2+A=\left[\begin{array}{cc}3& 4\\ -5& 7\end{array}\right]\left[\begin{array}{cc}3& 4\\ -5& 7\end{array}\right]+\left[\begin{array}{cc}3& 4\\ -5& 7\end{array}\right]$
$=\left[\begin{array}{cc}9-20& 12+28\\ -15-35& -20+49\end{array}\right]+\left[\begin{array}{cc}3& 4\\ -5& 7\end{array}\right]$
$\therefore A^2+A=\left[\begin{array}{cc}-8& 44\\ -55& 36\end{array}\right]$