Problem

A = [a_{ij}]_{2 \times 2}

where

a_{ij} = \begin{cases} i + j, & i \neq j \\ i^2 - 2j, & i = j \end{cases}

then

A^{-1}

is equal to : (a)

\frac{1}{9} \begin{bmatrix} 0 & 3 \\ 3 & 1 \end{bmatrix}

(b)

\frac{1}{9} \begin{bmatrix} 0 & -3 \\ 3 & -1 \end{bmatrix}

(c)

\frac{1}{9} \begin{bmatrix} 0 & -3 \\ -3 & -1 \end{bmatrix}

(d)

\frac{1}{3} \begin{bmatrix} 0 & 3 \\ 3 & 1 \end{bmatrix}