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A imc-like matrix problem

Source: Brazilian Math Olympiad 2005, Problem 1

October 24, 2005
linear algebramatrixalgebrapolynomialfunctionlinear algebra unsolved

Problem Statement

Determine the number of possible values for the determinant of AA, given that AA is a n×nn\times n matrix with real entries such that A3−A2−3A+2I=0A^3 - A^2 - 3A + 2I = 0, where II is the identity and 00 is the all-zero matrix.
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