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Found problems: 1

2013 Bogdan Stan, 3
Let be four $ n\times n $ real matrices $ A,B,C,D $ having the property that $ C+D\sqrt{-1} $ is the inverse of $ A+B\sqrt{-1} . $ Show that $ \left| \det\left( A+B\sqrt{-1} \right) \right|^2\cdot\left| \det C \right| =\det A. $ [i]Vasile Pop[/i]
eigenvalue matries matrices linear algebra