Q.If $A+B=\begin{bmatrix}7 & 4\\8 & 9\end{bmatrix}$ and $A-B=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}$ then the value of $A$ is ....... (A) $\begin{bmatrix}3 & 1\\4 & 3\end{bmatrix}$ (B) $\begin{bmatrix}4 & 3\\4 & 6\end{bmatrix}$ (C) $\begin{bmatrix}6 & 2\\8 & 6\end{bmatrix}$ (D) $\begin{bmatrix}7 & 6\\8 & 12\end{bmatrix}$

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 …