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Existence of an array c

Source: Brazilian university Olympiad-2019 #1

November 14, 2019
college contestsMatriceslinear algebrapolynomialBrazilian Undergrad MO 2019Brazilian Undergrad MO

Problem Statement

Let I I and 0 0 be the square identity and null matrices, both of size 2019 2019 . There is a square matrix AA with rational entries and size 2019 2019 such that: a) A3+6A2−2I=0 A ^ 3 + 6A ^ 2-2I = 0 ? b) A4+6A3−2I=0 A ^ 4 + 6A ^ 3-2I = 0 ?
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