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The adjoint

Source: RMO 2006

April 17, 2006
linear algebramatrixvectorlinear algebra unsolved

Problem Statement

Let AA be a n×nn\times n matrix with complex elements and let A⋆A^\star be the classical adjoint of AA. Prove that if there exists a positive integer mm such that (A⋆)m=0n(A^\star)^m = 0_n then (A⋆)2=0n(A^\star)^2 = 0_n. Marian Ionescu, Pitesti
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