Let A=[a ij ] be a matrix of order 3 × 3, with a ij =(√(2))^(i+j). If the sum of all the elements in the third row of A² is α+β√(2), α, β Z, then α+β is equal to:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q130

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

Let

A=\left[a_{ij}\right]

be a matrix of order

3 \times 3

, with

a_{ij}=(\sqrt{2})^{i+j}

. If the sum of all the elements in the third row of

A^2

\alpha+\beta\sqrt{2}

\alpha, \beta \in \mathbb{Z}

, then

\alpha+\beta

is equal to: