Transposing a magic square preserves magicness

Transposition. If $A$ is a magic square of line sum $S$, so is its transpose $A^{\mathsf T}$, with the same line sum.

The square is a symmetry of the $n\times n$ grid, so it permutes the lines: rows of $A^{\mathsf T}$ are the columns of $A$ and vice versa, while each main diagonal is fixed. Hence every line of $A^{\mathsf T}$ is a line of $A$ and still sums to $S$, and the same holds verbatim for panmagic (pandiagonal) squares, whose broken diagonals are also carried to broken diagonals.

Formalization Note transpose is the entrywise flip $(i,j)\mapsto(j,i)$ from Definitions.Def_MagicSquaresTransforms. The four line sums are tracked by rowSum_transpose, colSum_transpose, diagSum_transpose and antiDiagSum_transpose; the anti-diagonal case uses that $i\mapsto n-1-i$ is a bijection of $\mathrm{Fin}\,n$, so reindexing the sum is legitimate.