Types of matrices - One Line Questions

1. If A is a symmetric matrix, then A^T = ? — A
2. Any matrix A can be expressed as the sum of a symmetric and a skew-symmetric matrix. The symmetric part is given by: — (A + A^T)/2
3. Any matrix A can be expressed as the sum of a symmetric and a skew-symmetric matrix. The skew-symmetric part is given by: — (A - A^T)/2
4. For a skew-symmetric matrix A, the diagonal elements must be: — Zero
5. What is the order of a null matrix if it is also a square matrix? — nxn
6. If A is a skew-symmetric matrix, then A^T = ? — -A
7. If A is an orthogonal matrix, then A⁻¹ is equal to: — A^T
8. A matrix A is orthogonal if: — A^T A = I
9. For a symmetric matrix A, the elements satisfy the condition: — a_ij = a_ji
10. A triangular matrix is also a diagonal matrix if: — All its non-diagonal elements are zero
11. Which type of matrix has only one row? — Row matrix
12. A square matrix where all the elements are identical and non-zero is a: — Scalar matrix
13. Which of the following is NOT a type of square matrix? — Row matrix
14. If A = [[5, 0], [0, 5]], this is an example of a: — Scalar matrix
15. In a diagonal matrix, the elements a_ij are zero when: — i ≠ j
16. In an upper triangular matrix, the elements a_ij are zero when: — i > j
17. In a lower triangular matrix, the elements a_ij are zero when: — i < j
18. The identity matrix of order 2x2 is denoted by: — I₂
19. A matrix A is idempotent if A² = A. Which of the following is an idempotent matrix? — Both Identity and Null matrix
20. A matrix A is involutory if A² = I. Which of the following is an involutory matrix? — Identity matrix
21. A square matrix A is called nilpotent of index k if A^k = 0 and A^(k-1) ≠ 0. If k=1, then A is: — Null matrix
22. A matrix where all the elements below the main diagonal are zero is a: — Upper triangular matrix
23. If A = [[1, 2], [0, 3]], this is an example of a: — Upper triangular matrix
24. A matrix of order m x n is rectangular if: — m ≠ n
25. A matrix where all the elements are negative is called a: — Negative matrix
26. A scalar matrix where the diagonal elements are all 1 is called a: — Identity matrix
27. A matrix where all elements are equal is called a: — Constant matrix
28. A square matrix A is called periodic if A^k = I for some positive integer k. If k=1, then A is: — Identity matrix
29. A matrix where at least one element is non-zero is called a: — Non-zero matrix
30. If A = [[0, 0], [0, 0]], this is an example of a: — Null matrix
31. A matrix where all the elements are positive is called a: — Positive matrix
32. An identity matrix is always a: — Square matrix
33. A matrix where the number of rows is equal to the number of columns is known as a: — Square matrix
34. A matrix with only one column is called a: — Column matrix
35. A matrix of order 1x1 is always a: — Both Row and Column matrix
36. A matrix in which all the elements are zero is called a: — Null matrix
37. A square matrix where all the non-diagonal elements are zero is termed as a: — Diagonal matrix
38. Which type of matrix is both upper triangular and lower triangular? — Diagonal matrix
39. If A = [[2, 0], [0, 3]], this is an example of a: — Diagonal matrix
40. If A = [[1, 0], [0, 1]], this is an example of a: — All of the above
41. A matrix A is called Hermitian if A^θ = A. For a real matrix to be Hermitian, it must be: — Symmetric
42. A matrix that remains unchanged after transposition is: — Symmetric matrix
43. A matrix A is called skew-Hermitian if A^θ = -A, where A^θ is the conjugate transpose of A. For a real matrix to be skew-Hermitian, it must be: — Skew-symmetric
44. A matrix that becomes its negative after transposition is: — Skew-symmetric matrix
45. A square matrix is called skew-symmetric if its transpose is equal to: — The negative of the matrix
46. A square matrix is called symmetric if its transpose is equal to: — The matrix itself
47. Which type of matrix has all diagonal elements equal and all non-diagonal elements zero? — Scalar matrix
48. A matrix where all the elements above the main diagonal are zero is a: — Lower triangular matrix
49. If A = [[1, 2], [3, 4]], this is an example of a: — Rectangular matrix
50. If A = [[1, 0], [2, 3]], this is an example of a: — Lower triangular matrix
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