Question:
Write matrix A satisfying $A+\left[\begin{array}{rr}2 & 3 \\ -1 & 4\end{array}\right]=\left[\begin{array}{rr}3 & -6 \\ -3 & 8\end{array}\right]$.
Solution:
Given : $A+\left[\begin{array}{cc}2 & 3 \\ -1 & 4\end{array}\right]=\left[\begin{array}{cc}3 & -6 \\ -3 & 8\end{array}\right]$
$\Rightarrow A=\left[\begin{array}{cc}3 & -6 \\ -3 & 8\end{array}\right]-\left[\begin{array}{cc}2 & 3 \\ -1 & 4\end{array}\right]$
$\Rightarrow A=\left[\begin{array}{cc}3-2 & -6-3 \\ -3+1 & 8-4\end{array}\right]$
$\Rightarrow A=\left[\begin{array}{cc}1 & -9 \\ -2 & 4\end{array}\right]$