Let $A=\left[a_{i j}\right]$ be a real matrix of order $3 \times 3$, such that $a_{i 1}+a_{i 2}+a_{i 3}=1$, for $i=1,2,3$. Then, the sum of all the entries of the matrix $A^3$ is equal to: [JEE Main 2021, 22 Jul (Shift 2)]

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Let \(A=\left[a_{i j}\right]\) be a real matrix of order \(3 \times 3\), such that \(a_{i 1}+a_{i 2}+a_{i 3}=1\), for \(…

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