Question 132
Triana writes nine positive numbers, one in each cell of a $3 \times 3$ grid. The row sums and column sums are all equal. The row products and column products are also all equal to each other, but not necessarily equal to the row and column sums.
Show that each row and each column of Triana's matrix contains the same three (not necessarily distinct) numbers.
Show that each row and each column of Triana's matrix contains the same three (not necessarily distinct) numbers.