If \( A=\left[a_{i j}\right]_{2 \times 2} \) where \( a_{i j}=\left\{\begin{array}{cc}i+j & i \n...
If \( A=\left[a_{i j}\right]_{2 \times 2} \) where \( a_{i j}=\left\{\begin{array}{cc}i+j & i \neq j \\ i^{2}-2 j & i=j\end{array}\right. \), then \( A^{-1} \) is equal to -
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(A) \( \frac{1}{9}\left[\begin{array}{ll}0 & 3 \\ 3 & 1\end{array}\right] \)
(B) \( \frac{1}{9}\left[\begin{array}{ll}0 & -3 \\ 3 & -1\end{array}\right] \)
(C) \( \frac{1}{9}\left[\begin{array}{cc}0 & -3 \\ -3 & -1\end{array}\right] \)
(D) \( \frac{1}{3}\left[\begin{array}{ll}0 & 3 \\ 3 & 1\end{array}\right] \)
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