Thread: Permutation Matrix

A permutation matrix P is a 0,1-matrix having exactly one 1 in each row and column.
Prove that a square matrix of nonnegative integers can be expressed as the sum of k permutation matrices if and only if all rows and columns sum to k.

Can someone show this proof? Thanks a lot!!

Is this still relevant?

If I recall correctly, there's a proof of this in van Lint and Wilson's book on combinatorics, in the chapter on Hall's theorem.