Let A be a 3times3 matrix over complex numbers with trace 1 and determinant 1. Suppose, further, that one of the eigenvalues of A is 1. Which of the following statements is necessarily true?

(B) Every eigenvalue of A has absolute value 1.

Q28Section B (Part B)28 of 120

Eigenvalues — a 3x3 matrix with given trace and determinant

Let $A$ be a $3\times3$ matrix over complex numbers with trace 1 and determinant

Suppose, further, that one of the eigenvalues of $A$ is 1. Which of the following statements is necessarily true?

Pick an option to check your answer.

Keyboard: A–D answer · S solution · ←/→ previous/next