$A-B=\left[\begin{array}{ll}{1} & {2} \\ {3} & {4}\end{array}\right]$ ........$(i)$
$\Rightarrow A^{T}+B^{T}=\left[\begin{array}{ll}{1} & {2} \\ {3} & {4}\end{array}\right] $
$\Rightarrow(A+B)^{T}=\left[\begin{array}{ll}{1} & {2} \\ {3} & {4}\end{array}\right]$
$ \Rightarrow A + B = \left[ {\begin{array}{*{20}{l}}
1&3\\
2&4
\end{array}} \right]$ ......$(ii)$
Adding $(i)$ and $(ii)$ $A=\left[\begin{array}{ll}{1} & {\frac{5}{2}} \\ {\frac{5}{2}} & {4}\end{array}\right]$
$\therefore|A|=4-\frac{25}{4}=\frac{-9}{4}$
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$\frac{{dy}}{{dx}} + \frac{1}{x}\sin 2y = {x^3}\,{\cos ^2}\,y$ represented by family of curves which is is givey by