Q.If $A = [a_{ij}]$ is a $2 \times 2$ matrix, where $a_{ij} = \dfrac{1}{2}(i + 2j)^2$, then $A$ is

A matrix is a rectangular array of real numbers arranged in rows and columns, written $A=[a_{ij}]$, where the subscript $i$ names the row and $j$ names the column in which the entry $a_{ij}$ sits -- the row index is always written first. If a matrix has $m$ rows and $n$ columns it is said to have order $m\times n$, and it contains exactly $mn$ elements in total. Order is an ordered pair, so an $m\times n$ matrix and an $n\times m$ matrix are considered different orders unless $m=n$; consequently a given element-count can correspond to several distinct possible order …