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Tables in which each entry is the product of its neighbors

Source: 2nd European Mathematical Cup, Problem 1

December 16, 2013
linear algebramatrixalgebra proposedalgebra

Problem Statement

In each field of a table there is a real number. We call such n×nn \times n table silly if each entry equals the product of all the numbers in the neighbouring fields.
a) Find all 2×22 \times 2 silly tables. b) Find all 3×33 \times 3 silly tables.
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