Mathematics · Linear Algebra
Let A be a 3 × 3 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?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The characteristic polynomial of A has repeated roots.✓
- 2Every eigenvalue of A has absolute value 1.
- 3A does not have any eigenvalue on the imaginary axis.
- 4A2 is the identity matrix.
Correct answer
The characteristic polynomial of A has repeated roots.
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