Let \(A = [a_{ij}]_{n \times n}\) be a matrix, then match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | \(|A| = 0\) | (I) | A is a symmetric matrix |
| (B) | \(|A| \ne 0\) | (II) | A is a skew-symmetric matrix |
| (C) | \(A^T = A\) | (III) | A is a singular matrix |
| (D) | \(A^T = -A\) | (IV) | A is a non-singular matrix |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
Each item is a definition of a type of square matrix.
(A) \(|A| = 0\)
This matches (III) A is a singular matrix. A matrix with zero determinant is called singular.
(B) \(|A| \ne 0\)
This matches (IV) A is a non-singular matrix. A matrix with non-zero determinant is called non-singular.
(C) \(A^T = A\)
This matches (I) A is a symmetric matrix, by the definition of a symmetric matrix.
(D) \(A^T = -A\)
This matches (II) A is a skew-symmetric matrix, by the definition of a skew-symmetric matrix.
So the matching is (A)-(III), (B)-(IV), (C)-(I), (D)-(II).