Let A = (a_{ij})_{1 leq i, j leq 3} be a 3 ti | vedclass

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(B) Given that $A$ is a $3 	imes 3$ matrix such that the sum of elements in each row is $1$. This can be written as $A \cdot \mathbf{u} = \mathbf{u}$

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sum of each row of $A^{-1}$ is $1$

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(B) Given that $A$ is a $3 	imes 3$ matrix such that the sum of elements in each row is $1$. This can be written as $A \cdot \mathbf{u} = \mathbf{u}$,where $\mathbf{u} = [1, 1, 1]^T$ is a column vector of ones.Since $A$ is invertible,we can multiply both sides by $A^{-1}$:$A^{-1} (A \cdot \mathbf{u}) = A^{-1} \cdot \mathbf{u}$$(A^{-1} A) \cdot \mathbf{u} = A^{-1} \cdot \mathbf{u}$$I \cdot \mathbf{u} = A^{-1} \cdot \mathbf{u}$$\mathbf{u} = A^{-1} \cdot \mathbf{u}$This equation implies that the sum of the elements in each row of $A^{-1}$ is equal to the corresponding element in the vector $\mathbf{u}$,which is $1$. Therefore,the sum of each row of $A^{-1}$ is $1$.

Let $A = (a_{ij})_{1 \leq i, j \leq 3}$ be a $3 \times 3$ invertible matrix where each $a_{ij}$ is a real number. Denote the inverse of the matrix $A$ by $A^{-1}$. If $\sum_{j=1}^3 a_{ij} = 1$ for $1 \leq i \leq 3$,then:

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