jee-main 2025 Q5

jee-main · India · session1_29jan_shift2 Matrices Matrix Power Computation and Application
Let $A = \left[ a _ { i j } \right]$ 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 $\alpha + \beta \sqrt { 2 } , \alpha , \beta \in \mathbf { Z }$, then $\alpha + \beta$ is equal to :
(1) 280
(2) 224
(3) 210
(4) 168
Let $A = \left[ a _ { i j } \right]$ 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 $\alpha + \beta \sqrt { 2 } , \alpha , \beta \in \mathbf { Z }$, then $\alpha + \beta$ is equal to :\\
(1) 280\\
(2) 224\\
(3) 210\\
(4) 168