Let A be a 4 × 4 real matrix whose minimal polynomial is x 2 + x + 1 and let B = A + I 4 , where I 4 is the 4 × 4 identity matrix. Which of the following statements is necessarily true?

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Mathematics · Linear Algebra

Let A be a 4 × 4 real matrix whose minimal polynomial is x 2 + x + 1 and let B = A + I 4 , where I 4 is the 4 × 4 identity matrix. Which of the following statements is necessarily true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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3B 3 = I 4

Correct answer

The minimal polynomial of B is x 2 - x + 1

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Answer 1

The minimal polynomial of B is x 2 + x + 1

Answer 2

The minimal polynomial of B is x 2 - x + 1

Answer 3

B 3 + I 4 = 0

Let A be a 4 × 4 real matrix whose minimal polynomial is x 2 + x + 1 and let B = A + I 4 , where I 4 is the 4 × 4 identity matrix. Which of the following statements is necessarily true?

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Let A be a 4 &times; 4 real matrix whose minimal polynomial is x 2 + x + 1 and let B = A + I 4 , where I 4 is the 4 &times; 4 identity matrix. Which of the following statements is necessarily true?

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Let A be a 4 × 4 real matrix whose minimal polynomial is x 2 + x + 1 and let B = A + I 4 , where I 4 is the 4 × 4 identity matrix. Which of the following statements is necessarily true?