Q.If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$ and $B=\begin{bmatrix}5&6\\7&8\end{bmatrix}$, find $3A-2B$.

Addition of two matrices of the same order is defined entrywise, $A+B=[a_{ij}+b_{ij}]$, and is undefined if the orders differ. Scalar multiplication of a matrix $A$ by a real number $k$ is likewise entrywise, $kA=[k\,a_{ij}]$, and subtraction $A-B$ is defined as $A+(-1)B$. Both operations satisfy laws that directly mirror ordinary real-number arithmetic: addition is commutative ($A+B=B+A$) and associative ($(A+B)+C=A+(B+C)$), has an additive identity (the zero matrix) and additive inverses ($-A$), and scalar multiplication distribute …