MathDB

n^2

real numbers are written in a square

n \times n

table so that the sum of the numbers in each row and column equals zero. A move is to add a row to one column and subtract it from another (so if the entries are

a_{ij}

and we select row

i

, column

h

and column

k

, then column h becomes

a_{1h} + a_{i1}, a_{2h} + a_{i2}, ... , a_{nh} + a_{in}

, column

k

becomes

a_{1k} - a_{i1}, a_{2k} - a_{i2}, ... , a_{nk} - a_{in}

, and the other entries are unchanged). Show that we can make all the entries zero by a series of moves.

Problem Statement