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Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{-1}$.

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Consider any matrix which is invertible say 2*2 in which sum of rows is 1, what we get is sum of all elements of A-1 as 2. 

similarly u can check it for a 3*3 matrix it comes out to be 3.

and for 4*4 it comes out to be 4

and so on for 5*5 matrix.

and we can conclude that its equal to n for n*n matrix.

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