Exercise 5

A square matrix is semimagic if the rows and columns add to the same value, that is, if we drop the condition on the diagonals.

• (a)  Show that the set of semimagic squares $\mathscr{H}_{n}$ is a subspace of $\mathcal{M}_{n\!\times\!n}$.     (b)  Show that the set $\mathscr{H}_{n,0}$ of $n\!\times\!n$ semimagic squares with magic number $0$ is also a subspace of $\mathcal{M}_{n\!\times\!n}$.