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Sum of a matrix with its adjugate

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October 28, 2019
linear algebramatrixadjugategeneral linear matrix

Problem Statement

Let be an odd integer n≥3 n\ge 3 and an n×n n\times n real matrix A A whose determinant is positive and such that A+adjA=2A−1. A+\text{adj} A=2A^{-1} . Prove that A2010+adj2010A=2A−2010. A^{2010} +\text{adj}^{2010} A =2A^{-2010} .
Lucian Petrescu
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