7

Part of 2024 IMC

Problems(1)

Finding det(AB) if A+B=I and (A^2+B^2)(A^4+B^4)=A^5+B^5

Source: IMC 2024, Problem 7

n

be a positive integer. Suppose that

A

B

n \times n

matrices with complex entries such that

A+B=I

I

is the identity matrix) and

(A^2+B^2)(A^4+B^4)=A^5+B^5.

Find all possible values of

\det(AB)

n

linear algebradeterminantMatrices