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5

Part of 2021 IMC

Problems(1)

IMC 2021 P5: 2021B=A^m+B^2

Source: IMC 2021 P5

8/5/2021
Let AA be a real n×nn \times n matrix and suppose that for every positive integer mm there exists a real symmetric matrix BB such that
2021B=Am+B2.2021B = A^m+B^2.
Prove that ∣detA∣≤1|\text{det} A| \leq 1.
linear algebraIMC 2021matrixsymmetric matrix