Q.If $\begin{bmatrix}5 & 7\\x & 1\\2 & 6\end{bmatrix}-\begin{bmatrix}1 & 2\\-3 & 5\\2 & y\end{bmatrix}=\begin{bmatrix}4 & 5\\4 & -4\\0 & 4\end{bmatrix}$ then ...... (A) $x=1,y=-2$ (B) $x=-1,y=2$ (C) $x=1,y=2$ (D) $x=-1,y=-2$

Matrices of the same order can be checked for equality ($A=B$ iff every corresponding entry matches), added ($A+B=[a_{ij}+b_{ij}]$, entry-by-entry, undefined for mismatched orders), subtracted ($A-B=A+(-B)$), and scaled by a number ($kA=[k\,a_{ij}]$, every entry multiplied by $k$). These operations obey familiar-looking laws — addition is commutative ($A+B=B+A$) and associative ($(A+B)+C=A+(B+C)$), the zero matrix is the additive identity, $-A$ is the additive inverse, and scalar multiplication distributes over both matrix sums and scalar sums. The most common use is solving a linear matrix equation for an unknown matrix $X$ (e.g. $3A-4B+5X=C$): treat $X$ exac …