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Easy one

Source: IMC 1999 day 1 problem 1

November 19, 2005
linear algebramatrixalgebrapolynomialcomplex numbers

Problem Statement

a) Show that ∀n∈N0,∃A∈Rn×n:A3=A+I\forall n \in \mathbb{N}_0, \exists A \in \mathbb{R}^{n\times n}: A^3=A+I. b) Show that det⁡(A)>0,∀A\det(A)>0, \forall A fulfilling the above condition.
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