Let $A = [a_{ij}]_{n×n}$ be a matr

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

Let $A = [a_{ij}]_{n×n}$ be a matrix, then match List-I with List-II

List-I	List-II
(A) $\|A\|= 0$	(I) A is a symmetric matrix
(B) $\|A\|≠0$	(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:

Options:

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Correct Answer:

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Explanation:

The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

List-I	List-II
(A) $\|A\|= 0$	(III) A is a singular matrix
(B) $\|A\|≠0$	(IV) A is a non-singular matrix
(C) $A^T = A$	(I) A is a symmetric matrix
(D) $A^T=-A$	(II) A is a skew-symmetric matrix

Given: Let A = [a_ij]_n×n be a matrix.

(A) |A| = 0: If the determinant of a matrix is 0, then the matrix is called singular.
So, (A) ⟶ (III)

(B) |A| ≠ 0: If the determinant of a matrix is non-zero, then the matrix is called non-singular.
So, (B) ⟶ (IV)

(C) A^T = A: This is the definition of a symmetric matrix.
So, (C) ⟶ (I)

(D) A^T = –A: This is the definition of a skew-symmetric matrix.
So, (D) ⟶ (II)