Mathematics · Linear Algebra
Let A, B be 2 × 2 matrices with real entries, and M = AB - BA. Let I2 denote the 2 × 2 identity matrix. Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There exists λ ∈ ℝ such that M2 = λI2.✓
- 2If A and B are diagonalizable over ℝ, then there exists λ ∈ ℝ such that M = λI2.
- 3If A and B are diagonalizable over ℝ, then M is diagonalizable over ℝ.
- 4If A and B are upper triangular, then M is diagonalizable over ℝ.
Correct answer
There exists λ ∈ ℝ such that M2 = λI2.
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