If X+Y= […] and X-Y= […] . Then X and Y are :

The correct answer is Option (1) → $X=\begin{bmatrix}5 & 0\\1 & 4\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$

$X+Y=\begin{bmatrix}7 & 0\\2 & 5\end{bmatrix}$ ....(1)

$X-Y=\begin{bmatrix}3 & 0 \\0 & 3\end{bmatrix}$  ....(2)

$X+Y+X-Y=\begin{bmatrix}10 & 0\\2 & 8\end{bmatrix}$

$2X=\begin{bmatrix}10 & 0\\2 & 8\end{bmatrix}⇒X=\begin{bmatrix}5& 0\\1 & 4\end{bmatrix}$

so from (1)

$Y=\begin{bmatrix}7& 0\\2 & 5\end{bmatrix}-\begin{bmatrix}5& 0\\1 & 4\end{bmatrix}$

$Y=\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$