Algebra

Matrices & Determinants

Medium

core

For a square matrix $A$ of order 3, if $|A| = 2$ , then $|adj\ 2A| =$

256

✅ Correct Option: 4

For an $n \times n$ matrix $A$ , the determinant of a scalar multiple is given by $|kA| = k^n \times |A|$ .

For an $n \times n$ matrix $A$ , the determinant of the adjoint matrix is given by $|adj\ A| = |A|^{n-1}$ .

Given: Order of matrix $A$ is $3$ and $|A| = 2$

To find $|adj\ 2A|$ , first find $|2A|$ .

$|2A| = 2^3 \times |A|$

$|2A| = 8 \times 2$

$|2A| = 16$

Now treat $2A$ as a single matrix. Since $2A$ is also a $3 \times 3$ matrix:

$|adj\ 2A| = |2A|^{3-1}$

$|adj\ 2A| = |2A|^2$

$|adj\ 2A| = (16)^2$

$|adj\ 2A| = 256$

Therefore, $|adj\ 2A| = 256$ .

2025: 19 May Shift 1

Which of the following statements are correct?

(A) If A is a square matrix, then $|A^2| = |A|^2$ .

(B) If A and B are square matrices of the same order, then det (AB) = det (A) + det (B).

(D) If the matrix $\begin{bmatrix} 5 -x & x -1 \\ 3 &5 \end{bmatrix}$ is singular, then the value of x is 7/2.

Choose the correct answer from the options given below:

2026: 25 May Shift 1

For a square matrix $A$ of order 3, if $\lvert A\rvert = -3$ , then $\lvert 4\,adj A\rvert$ is equal to

2023: 30 May Shift 3

If $A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 \\ 3 & -4 \\ 2 & 4 \end{bmatrix}$ then product AB is :

2022: 30 Aug Shift 1

The value of $y$ is

2026: 12 May Shift 2

The matrix which is both symmetric and skew-symmetric, is a:

2026: 25 May Shift 1

If A is a $2 \times 3$ matrix and B is a matrix such that $A^{T}B$ and $BA^{T}$ are both defined. Then order of B is

For a square matrix AAA of order 3, if ∣A∣=2|A| = 2∣A∣=2, then ∣adj 2A∣=|adj\ 2A| =∣adj 2A∣=

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

For a square matrix $A$ of order 3, if $|A| = 2$ , then $|adj\ 2A| =$