Constructing a $3 \times 3$ matrix $A = [a_{i j}]$ whose elements are given by $a_{i j} = {(i + j)}^{2}$ is

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$[\begin{matrix} 26 & 25 & 16 \\ 16 & 9 & 25 \\ 9 & 4 & 16 \end{matrix}]$

$[\begin{matrix} 25 & 16 & 9 \\ 26 & 25 & 16 \\ 16 & 4 & 9 \end{matrix}]$

$[\begin{matrix} 16 & 26 & 25 \\ 9 & 16 & 26 \\ 4 & 25 & 16 \end{matrix}]$

$[\begin{matrix} 4 & 9 & 16 \\ 9 & 16 & 25 \\ 16 & 25 & 36 \end{matrix}]$

answer is C.

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Detailed Solution

$A = (a_{i j}) \times_{3}$

$a : j = {(i + j)}^{2}$

$A = [\begin{matrix} {(1 + 1)}^{2} & {(1 + 2)}^{2} & {(1 + 3)}^{2} \\ {(2 + 1)}^{2} & {(2 + 2)}^{2} & {(2 + 3)}^{2} \\ {(3 + 1)}^{2} & {(3 + 2)}^{2} & {(3 + 3)}^{2} \end{matrix}]$

$= [\begin{matrix} 4 & 9 & 16 \\ 9 & 16 & 25 \\ 16 & 25 & 36 \end{matrix}]$

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