If A = bmatrix 2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0 bmatrix, then the value of det (2A) is Option 1: 72 Option 2: -144 Option 3: 288 Option 4: 144

Answer: 288. Solution: For any n x n matrix: (kA) = k^n x (A) Since A is a 3 x 3 matrix: (2A) = 2^3 x (A) (2A) = 8 x (A) Given: A = bmatrix 2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0 bmatrix Expanding along Row 3 (which contains the most zeros): (A) = 0 * C_31 - (-4) * C_32 + 0 * C_33 (A) = 4 * M_32 where M_32 is the minor obtained by removing Row 3 and Column 2. M_32 = vmatrix 2 & 3 \\ -1 & 3 vmatrix M_32 = (2)(3) - (3)(-1) M_32 = 6 - (-3) M_32 = 6 + 3 M_32 = 9 (A) = 4 x 9 (A) = 36 (2A) = 8 x (A) (2A) = 8 x 36 (2A) = 288 Therefore, the value of (2A) = 288.

Algebra

Matrices & Determinants

Medium

core

If $A = \begin{bmatrix} 2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0 \end{bmatrix}$ , then the value of det (2A) is

-144

288

144

✅ Correct Option: 3

For any $n \times n$ matrix: $\det(kA) = k^n \times \det(A)$

Since $A$ is a $3 \times 3$ matrix:

$\det(2A) = 2^3 \times \det(A)$

$\det(2A) = 8 \times \det(A)$

Given: $A = \begin{bmatrix} 2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0 \end{bmatrix}$

Expanding along Row 3 (which contains the most zeros):

$\det(A) = 0 \cdot C_{31} - (-4) \cdot C_{32} + 0 \cdot C_{33}$

$\det(A) = 4 \cdot M_{32}$

where $M_{32}$ is the minor obtained by removing Row 3 and Column 2.

$M_{32} = \begin{vmatrix} 2 & 3 \\ -1 & 3 \end{vmatrix}$

$M_{32} = (2)(3) - (3)(-1)$

$M_{32} = 6 - (-3)$

$M_{32} = 6 + 3$

$M_{32} = 9$

$\det(A) = 4 \times 9$

$\det(A) = 36$

$\det(2A) = 8 \times \det(A)$

$\det(2A) = 8 \times 36$

$\det(2A) = 288$

Therefore, the value of $\det(2A) = 288$ .

2025: 16 May Shift 1

The value of $\begin{vmatrix} 1 & bc & bc(b+c) \\ 1 & ca & ca(c+a) \\ 1 & ab & ab(a+b) \end{vmatrix}$ is

2026: 18 May Shift 2

If matrix $A=\begin{bmatrix} 5 & 2 & 3 \\ 4 & 1 & 2 \\ 7 & 6 & 0 \end{bmatrix}$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert A \vert$	I.	$16$
B.	Minor of $a_{23}$	II.	$27$
C.	Cofactor of $a_{32}$	III.	$19$
D.	If $a_{23}$ is interchanged with $a_{32}$ , then $\vert A \vert$	IV.	$2$

Choose the correct answer from the options given below:

2026: 15 May Shift 1

If $A$ is a square matrix such that $|A| \neq 0$ and $A^2 - A + 2I = 0$ then $A^{-1}$ is equal to :(where $I$ is an identity matrix of order as order of matrix $A$ )

2023: 15 June Shift 2

Match List - I with List - II. If $A = \begin{vmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{vmatrix}$

List - I	List - II
(A) $M_{23}$	(I) $-17$
(B) $A_{32} + a_{13}$	(II) $-1$
(C) A	(III) 0
(D) $a_{13}A_{12} + a_{23}A_{22} + a_{33}A_{32}$	(IV) 12

Choose the correct answer from the options given below :

2026: 30 May Shift 2

The value of $\begin{vmatrix}x & a & a\\a & x & a\\a & a & x\end{vmatrix}$ is equal to:

2025: 16 May Shift 1

Let A = [aᵢⱼ]ₙₓₙ and B = [bᵢⱼ]ₙₓₙ. Then which of the following is/are true?

(A) AB = BA

(B) (AB)⁻¹ = B⁻¹ A⁻¹

(D) AB = 0 ⇒ A = 0 or B = 0

Choose the correct answer from the options given below:

If A=[203−1130−40]A = \begin{bmatrix} 2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0 \end{bmatrix}A=​2−10​01−4​330​​, then the value of det (2A) is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} 2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0 \end{bmatrix}$ , then the value of det (2A) is