Ans: 1. The sum of the entries of each row of the inverse of $A$ is $1$.
Explanation:
Let me first define a vector $e$, which is a vector of all $1$s. (Vector is nothing but a column matrix)
so,
$e = \begin{bmatrix} 1\\ 1\\ ..\\ 1 \end{bmatrix}_{10 \times 1}$
Now, what will be $Ae =\ ?$
Think about it.
It turns out, that since the sum of each row of $A$ is $1$, $Ae$ will be equal to $e$. This is an important point.
so,
$Ae = e$
Multiply both sides by $A^{-1}$
$\implies A^{-1}Ae = A^{-1}e$
$\implies e = A^{-1}e$
$\implies A^{-1}e = e$
The above equation means that when we multiply $A^{-1}$ with $e$, we get $e$. What this implies?
This means that the sum of each row in $A^{-1}$ is $1$.