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MathNet 1985 — Part 01 Question 13

Math Olympiad Vault · MathNet 1985 — Part 01

Question 13

We will say that a square matrix is of a constant sum if the sum of the elements of each row, of each column, and of each diagonal, are equal values. Similarly, a square matrix is of constant product if the products of the elements of each row, each column and each diagonal are equal. Determine the square matrices of order $3$ over $\mathbb{R}$ which are both sum and constant product.