exists a 3x3 matrix with constant sums and constant products also ?
Source: Spanish Mathematical Olympiad 1985 P8
August 2, 2018
linear algebramatrixmagic squarecombinatorics
Problem Statement
A square matrix is sum-magic if the sum of all elements in each row, column and major diagonal is constant. Similarly, a square matrix is product-magic if the product of all elements in each row, column and major diagonal is constant.
Determine if there exist matrices of real numbers which are both sum-magic and product-magic.