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A^3=-I, BA^2+BA=C^6+C+I, C symmetric - OIMU 2005 Problem 2

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September 3, 2010
linear algebramatrixalgebrapolynomiallinear algebra unsolved

Problem Statement

Let A,B,CA,B,C be real square matrices of order nn such that A3=āˆ’IA^3=-I, BA2+BA=C6+C+IBA^2+BA=C^6+C+I and CC is symmetric. Is it possible that n=2005n=2005?
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