I had some trouble to understand easily @f" answer, so I'll post a more intuitive one.
The matrix is:
$$\begin{bmatrix}a_{0,0} & a_{0,1}&... &a_{0,10}\\a_{1,0}&...&..&...\\...&...&...&...\\a_{10,0} &...&...& a_{10,10}\end{bmatrix}$$
$$\text{row sum }r_i=\sum_{k=0}^{10}{a_{i,k}}\qquad i=0...10$$
$$\text{column sum }c_i=\sum_{k=0}^{10}{a_{k,i}}\qquad i=0...10$$
we define
$$\text{sum of the sums of the rows }R=\sum_{i=0}^{10}{r_{i}}$$
and
$$\text{sum of the sums of the columns }C=\sum_{i=0}^{10}{c_{i}}$$
$(1)$ From the question we know that $C+R=\text{sum of first 22 primes}=2n + 1= 791$
$(2)$ From the construction of $C$ and $R$ we know that $C=R$ since they are the sum of all of the values of the matrix. Therefore their sum must be in the form $C+R= 2C = 2R = 2n$ which is in contradiction with $(1)$
Therefore, the row and column sums cannot be the first 22 prime numbers. -@f"
0,1,4,6,8,9,10
, right? $\endgroup$