Question:
Let \( A \) be a \( 3 \times 3 \) real matrix. Suppose that 1 and 2 are characteristic roots of \( A \), and 12 is a characteristic root of \( A + A^2 \). Then which of the following statements is/are correct?
Let \( A \) be a \( 3 \times 3 \) real matrix. Suppose that 1 and 2 are characteristic roots of \( A \), and 12 is a characteristic root of \( A + A^2 \). Then which of the following statements is/are correct?
Updated On: Oct 1, 2024
- \(\det(A) \neq 0\)
- \(\det(A + A^2) \neq 0\)
- \(\det(A) = 0\)
- trace of \((A + A^2)\) is 20
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The Correct Option is A, B, D
Solution and Explanation
The correct option is (A): \(\det(A) \neq 0\),(B): \(\det(A + A^2) \neq 0\) ,(D): trace of \((A + A^2)\) is 20
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