If A = bmatrix1 & 2\\ 0 & 3bmatrix then, A. adj A, is Option 1: 3 Option 2: 6 Option 3: 9 Option 4: 12

Answer: 9. Solution: Given A = bmatrix1 & 2\\ 0 & 3bmatrix For any matrix multiplication:, A * B, =, A, x, B, Therefore:, A * adj(A), =, A, x, adj(A), For a 2×2 matrix bmatrixa & b\\ c & dbmatrix, the determinant is ad - bc, A, = (1)(3) - (2)(0), A, = 3 - 0, A, = 3 For an n×n matrix, adj(A), =, A, ^(n-1) Since A is a 2×2 matrix, n = 2:, adj(A), =, A, ^(2-1), adj(A), =, A, ^1, adj(A), = 3, A * adj(A), =, A, x, adj(A), A * adj(A), = 3 x 3, A * adj(A), = 9 Therefore, A adj A, = 9

Algebra

Matrices & Determinants

Medium

applied

If $A = \begin{bmatrix}1 & 2\\ 0 & 3\end{bmatrix}$ then $|A. adj A|$ is

✅ Correct Option: 3

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

For any matrix multiplication: $|A \cdot B| = |A| \times |B|$

Therefore: $|A \cdot adj(A)| = |A| \times |adj(A)|$

For a 2×2 matrix $\begin{bmatrix}a & b\\ c & d\end{bmatrix}$ , the determinant is $ad - bc$

$|A| = (1)(3) - (2)(0)$

$|A| = 3 - 0$

$|A| = 3$

For an n×n matrix, $|adj(A)| = |A|^{n-1}$

Since A is a 2×2 matrix, n = 2:

$|adj(A)| = |A|^{2-1}$

$|adj(A)| = |A|^{1}$

$|adj(A)| = 3$

$|A \cdot adj(A)| = |A| \times |adj(A)|$

$|A \cdot adj(A)| = 3 \times 3$

$|A \cdot adj(A)| = 9$

Therefore, $|A adj A| = 9$

2025: 15 May Shift 2

Let $A = [a_{ij}]$ be a square matrix, where $a_{ij} = \begin{cases} 0, & \text{when } i = j \\ 1, & \text{otherwise} \end{cases}$ . If |adj A| = |A|², then which of the following statements are correct?

(A) A is a skew symmetric matrix.

(B) A is a non-singular matrix.

(D) A is a symmetric matrix.

Choose the correct answer from the options given below:

2026: 22 May Shift 2

If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$ , where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

2026: 18 May Shift 2

If a matrix $A=\begin{bmatrix} 3 & -5 & 7 \\ 5 & 2 & 4 \\ -7 & -4 & 9 \end{bmatrix}$ is expressed as the sum of a symmetric matrix P and a skew symmetric matrix Q, then symmetric matrix P will be

2025: 13 May Shift 1

Which of the following is NOT correct?

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:

2026: 18 May Shift 1

If a matrix has 7 elements, then it can be a

(A) Scalar matrix

(B) Symmetric matrix

(D) Row matrix

Choose the correct answer from the options given below:

If A=[1203]A = \begin{bmatrix}1 & 2\\ 0 & 3\end{bmatrix}A=[10​23​] then ∣A.adjA∣|A. adj A|∣A.adjA∣ is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix}1 & 2\\ 0 & 3\end{bmatrix}$ then $|A. adj A|$ is