Let \(A = [a_{ij}]_{n \times n}\) be a matrix. Then
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | \(A^{T} = A\) | (I) | A is a singular matrix |
| (B) | \(A^{T} = -A\) | (II) | A is a non-singular matrix |
| (C) | \(|A| = 0\) | (III) | A is a skew symmetric matrix |
| (D) | \(|A| \ne 0\) | (IV) | A is a symmetric matrix |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
Each item is a definition.
(A) \(A^{T} = A\)
This matches (IV) A is a symmetric matrix. A matrix equal to its own transpose is symmetric.
(B) \(A^{T} = -A\)
This matches (III) A is a skew symmetric matrix. A matrix equal to the negative of its transpose is skew symmetric.
(C) \(|A| = 0\)
This matches (I) A is a singular matrix. A square matrix with zero determinant is singular.
(D) \(|A| \ne 0\)
This matches (II) A is a non-singular matrix. A square matrix with non-zero determinant is non-singular.
So the matching is (A)-(IV), (B)-(III), (C)-(I), (D)-(II).