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matrix

Source: Romania District Olympiad 2013,grade XI(problem 3)

March 14, 2013
linear algebramatrixabstract algebracomplex numbersalgebra proposedalgebra

Problem Statement

Let AA be an non-invertible of order nn, n>1n>1, with the elements in the set of complex numbers, with all the elements having the module equal with 1
a)Prove that, for n=3n=3, two rows or two columns of the AA matrix are proportional b)Does the conclusion from the previous exercise remains true for n=4n=4?
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