Sums of Squares of Lines of Order 3 Magic Square

Theorem
Consider the order 3 magic square:


 * The sums of the squares of the rows, when expressed as $3$-digit decimal numbers, are equal to the sums of the squares of those same rows of that same order 3 magic square when reflected in a vertical axis:


 * $\begin{array}{|c|c|c|}

\hline 6 & 7 & 2 \\ \hline 1 & 5 & 9 \\ \hline 8 & 3 & 4 \\ \hline \end{array}$

Similarly:


 * The sums of the squares of the columns, when expressed as $3$-digit decimal numbers, are equal to the sums of the squares of those same columns of that same order 3 magic square when reflected in a horizontal axis:


 * $\begin{array}{|c|c|c|}

\hline 4 & 3 & 8 \\ \hline 9 & 5 & 1 \\ \hline 2 & 7 & 6 \\ \hline \end{array}$

Proof
For the rows:

For the columns:

Also see

 * Sums of Squares of Diagonals of Order 3 Magic Square