Let A =[ a_ij ] be a real matrix of order 3 × 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…

Let $\displaystyle \mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a real matrix of order $\displaystyle 3 \times 3$, such that $\displaystyle \mathrm{a}_{\mathrm{i} 1}+\mathrm{a}_{\mathrm{i} 2}+\mathrm{a}_{\mathrm{i} 3}=1$, for $\displaystyle i=1,2,3$. Then, the sum of all the entries of the matrix $\displaystyle \mathrm{A}^3$ is equal to: