1. If matrix A = [[1, 2], [3, 4]], which of the following statements is true about its eigenvalues?
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2. Let A = [[2, 0], [0, 3]]. Which matrix B commutes with A (i.e., AB = BA)?
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3. Consider matrix A = [[0, 1], [-2, -3]]. What is the trace and determinant of A?
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4. For a 3×3 matrix A, if its rank is 2, what can be inferred?
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5. If a matrix A is orthogonal, which of the following is always true?
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6. If matrix A has eigenvalues 1, 2, and 3, what is the determinant of A?

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7. If A is a square matrix such that A^2 = I, what are the possible eigenvalues of A?
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8. Which of the following matrices is **not** invertible?
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9. If A is a 3×3 matrix and det(A) = 5, what is det(2A)?
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10. Which statement is true for any symmetric real matrix?
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11. If A is a 2×2 matrix and A is invertible, which of the following must also be invertible?
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12. What is the rank of the matrix [[1, 2], [2, 4]]?

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13. Which of the following matrices is symmetric?
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14. What is the trace of the matrix [[2, 1], [3, 4]]?

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15. Which transformation preserves the length of vectors?
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16. If A is diagonalizable, then it must have...
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17. Which of the following matrices is idempotent (A^2 = A)?
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18. What does the nullity of a matrix refer to?
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19. If matrix A is singular, what does it imply?
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20. The product of a matrix and its transpose is always...
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