Let $A=\left[{a}_{ij}\right]$ be a matrix of order $3 \times 3$, with $a_{i j}=(\sqrt{2})^{i+j}$. If the sum of all the elements in the third row of $A^2$ is $\alpha+\beta \sqrt{2}, \alpha, \beta \in Z$, then $\alpha+\beta$ is equal to :

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Let \(A=\left[{a}_{ij}\right]\) be a matrix of order \(3 \times 3\), with \(a_{i j}=(\sqrt{2})^{i+j}\). If the sum of al…

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