Let A =[ a_i j] be a matrix of order 3 × 3, with a_i j=(√ 2 )^i+j. If the sum of all the elements in the third row of A^2 is α+β √ 2, α, β ∈ Z, then…

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