Trace, product of matricesMedium

Matrix Powers and Row Element Sums

Let A = [a_ij] be a matrix of order 3 × 3, with ${a_{ij}} = {\left( {\sqrt 2 } \right)^{i + j}}$ . If the sum of all the elements in the third row of A² is $\alpha + \beta \sqrt 2$ , α, β ∈ Ζ, then α + β is equal to

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