CUET UG 2025 — Mathematics Algebra

2025mcqeasy

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

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

Official previous-year question

Held on 30 May 2025 · Verified 13 Jul 2026.

Options

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

Did you get this right?

Solution

$|A| = 0$ means the determinant is zero, which is the definition of a singular matrix.

$(A) \rightarrow (III)$

$|A| \neq 0$ means the determinant is non-zero, which is the definition of a non-singular matrix.

$(B) \rightarrow (IV)$

$A^T = A$ means the transpose equals the matrix itself, which is the definition of a symmetric matrix.

$(C) \rightarrow (I)$

$A^T = -A$ means the transpose equals the negative of the matrix, which is the definition of a skew-symmetric matrix.

$(D) \rightarrow (II)$

Final matching:

$(A) \rightarrow (III)$

$(B) \rightarrow (IV)$

$(C) \rightarrow (I)$

$(D) \rightarrow (II)$

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List-I

List-II

(A)

\vert A\vert = 0

(I)

A

is a symmetric matrix

(B)

\vert A\vert \neq 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

Solution

$|A| = 0$ means the determinant is zero, which is the definition of a singular matrix.

$(A) \rightarrow (III)$

$|A| \neq 0$ means the determinant is non-zero, which is the definition of a non-singular matrix.

$(B) \rightarrow (IV)$

$A^T = A$ means the transpose equals the matrix itself, which is the definition of a symmetric matrix.

$(C) \rightarrow (I)$

$A^T = -A$ means the transpose equals the negative of the matrix, which is the definition of a skew-symmetric matrix.

$(D) \rightarrow (II)$

Final matching:

$(A) \rightarrow (III)$

$(B) \rightarrow (IV)$

$(C) \rightarrow (I)$

$(D) \rightarrow (II)$

CUET UG 2025 — Mathematics Algebra

Options

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Solution

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CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra