If A is a square matrix of order 3 such that A( adj A) = bmatrix -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 bmatrix, then, A, is equal to Option 1: 2 Option 2: -8 Option 3: 8 Option 4: -2

Answer: -2. Solution: For any square matrix A of order n: A x (adj A) =, A, x I where, A, is the determinant of matrix A and I is the identity matrix. Given that: A(adj A) = bmatrix -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 bmatrix The matrix on the right has -2 on all diagonal elements and 0 elsewhere. bmatrix -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 bmatrix = -2 x bmatrix 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 bmatrix A(adj A) = -2I Using the property A x (adj A) =, A, x I:, A, x I = -2I Therefore:, A, = -2

Algebra

Matrices & Determinants

Medium

applied

If A is a square matrix of order 3 such that $A( {adj } A) = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ , then $|A|$ is equal to

-8

-2

✅ Correct Option: 4

For any square matrix $A$ of order $n$ :

$A \times (\text{adj } A) = |A| \times I$

where $|A|$ is the determinant of matrix $A$ and $I$ is the identity matrix.

Given that:

$A(\text{adj } A) = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$

The matrix on the right has $-2$ on all diagonal elements and $0$ elsewhere.

$\begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix} = -2 \times \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

$A(\text{adj } A) = -2I$

Using the property $A \times (\text{adj } A) = |A| \times I$ :

$|A| \times I = -2I$

Therefore:

$|A| = -2$

2026: 31 May Shift 2

If $\begin{bmatrix} 0 & x \\ 2 & 1 \end{bmatrix} + 2\begin{bmatrix} 3 & 1 \\ y & 0 \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 8 & 1 \end{bmatrix}$ , then the value of $2x+3y$ is :

2026: 19 May Shift 1

Given a matrix $A = \begin{bmatrix} 0 & 3 & -8 \\ -3 & 0 & 13 \\ 8 & -13 & 0 \end{bmatrix}$ . Which of the following statements is/are TRUE?

(A) The matrix A is a skew-symmetric matrix.

(B) The matrix A is a symmetric matrix.

(D) The matrix A is a non-singular matrix.

Choose the correct answer from the options given below:

2026: 19 May Shift 1

If $A = \begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix}$ , then which of the following statement(s) is/are TRUE?

(A) Matrix A is non-singular

(B) $|3A| = 54$

(D) $A^2 = \begin{bmatrix} -5 & -3 \\ 2 & -6 \end{bmatrix}$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

Given a matrix A of order 3x3. If |A|=3 then the value of |A(adj A)| is:

2025: 14 May Shift 2

If $A = \begin{bmatrix} 2 & -3 & 4 \\ -3 & 5 & x \\ 4 & 3 & 0 \end{bmatrix}$ is a symmetric matrix and $B = \begin{bmatrix} 0 & 2 & -10 \\ -2 & z & 6 \\ y & -6 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then the value of $(xy + yz + zx)$ is

2025: 15 May Shift 1

If A is an invertible matrix of order 2, then $\det(( {adj } A)^{-1})$ is equal to

If A is a square matrix of order 3 such that A(adjA)=[−2000−2000−2]A( {adj } A) = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}A(adjA)=​−200​0−20​00−2​​, then ∣A∣|A|∣A∣ is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If A is a square matrix of order 3 such that $A( {adj } A) = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ , then $|A|$ is equal to