Suppose that $S$ is a square such that the sum of the entries in each row is some number $R$, and the sum of the entries in each column is some number $C$. Prove that $S$ is in fact a magic square, i.e., $R = C$.
What I thought?
The sum of a row is $(1+..+n-1)n+(1+..+n)$, and the same for any col, hence the square in magic. Can someone verify this and help me elaborate on this.