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• 14:37, 23 January 2025 Andrei.Horvat talk contribs created page 27429 (Created page with "'''27429 (Radu Pop și Vasile Ienutaș, Baia Mare)''' ''Fie <math>A, B \in M_3(\mathbb{R})</math> cu proprietatea că <math>A^2 + B^2 = 2AB + BA</math>. Să se arate că'' <math> \det(4AB - BA) + \det(AB - 4BA) = 10\det(AB + 2BA) - 10\det(2AB + BA). </math> '''Soluție''' Avem <math> |\det(A + iB)|^2 = \det((A - iB)(A + iB)) = \det(A^2 + B^2 + i(AB - BA)) = \det(2AB + BA + i(AB - BA)). </math> Fie <math>f = \det(2AB + BA + X(AB - BA)) \in \mathbb{C}[X]</math>. Av...")