Mathematics · Linear Algebra
Let A and B be 2 × 2 real matrices. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If AB and BA have the same minimal polynomial, then either A or B must be invertible.
- 2If 0 is the only eigenvalue of A and of B, then 0 is the only eigenvalue of AB.
- 3If 0 is an eigenvalue of A, then 0 must be an eigenvalue of AB.
- 4If A is invertible, then AB and BA have the same minimal polynomial.✓
Correct answer
If A is invertible, then AB and BA have the same minimal polynomial.
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