Arrange the digits 2, 3, 4, 5, 6 and 7 in a 2×3 array (2 rows, 3 columns) so that the product of the two 3-digit numbers in each row is equal to the product of the three 2-digit numbers in each column. what is the sum of the 3-digit numbers in the rows?

i solved this problem (999) but i need mathematically proving it is the only solution possible.