# Construct a $2 \times 2$ matrix, $A=[a_{ij}],$whose elements are given by: $a_{ij}=\frac{(i+j)^2}{2}\qquad$
$\begin{array}{1 1} \begin{bmatrix}1 & \frac{9}{2}\\\frac{9}{2} & 8\end{bmatrix} \\\begin{bmatrix}2 & \frac{9}{2}\\\frac{9}{2} & 8\end{bmatrix} \\ \begin{bmatrix}2 & \frac{9}{3}\\\frac{9}{2} & 8\end{bmatrix} \\ \begin{bmatrix}2 & \frac{9}{2}\\\frac{9}{2} & -8\end{bmatrix} \end{array}$