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Idempotent

Source: IMC 2003 day 1 problem 3

October 14, 2005
algebrapolynomiallinear algebramatrixlinear algebra unsolved

Problem Statement

Let A∈Rn×nA\in\mathbb{R}^{n\times n} such that 3A3=A2+A+I3A^3=A^2+A+I. Show that the sequence AkA^k converges to an idempotent matrix. (idempotent: B2=BB^2=B)
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