If the matrix A = bmatrix & \\ - & bmatrix, then A^2 is equal to: Option 1: bmatrix 2 & 2 \\ - 2 & 2 bmatrix Option 2: bmatrix ^2 & ^2 \\ -^2 & ^2 bmatrix Option 3: bmatrix ^2 & ^2 \\ -^2 & ^2 bmatrix Option 4: bmatrix + & - \\ - & + bmatrix

Answer: bmatrix 2 & 2 \\ - 2 & 2 bmatrix. Solution: A is a rotation matrix by angle . Two rotations of compose to a rotation of 2. Direct multiplication confirms each entry uses the double-angle identities, giving 2 and 2 in place of and .

Algebra

Matrices & Determinants

Medium

core

If the matrix $A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$ , then $A^2$ is equal to:

$\begin{bmatrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \end{bmatrix}$

$\begin{bmatrix} \cos^2\theta & \sin^2\theta \\ -\sin^2\theta & \cos^2\theta \end{bmatrix}$

$\begin{bmatrix} \cos\theta^2 & \sin\theta^2 \\ -\sin\theta^2 & \cos\theta^2 \end{bmatrix}$

$\begin{bmatrix} \cos\theta+\sin\theta & \cos\theta-\sin\theta \\ \sin\theta-\cos\theta & \cos\theta+\sin\theta \end{bmatrix}$

✅ Correct Option: 1

$A$ is a rotation matrix by angle $\theta$ . Two rotations of $\theta$ compose to a rotation of $2\theta$ . Direct multiplication confirms each entry uses the double-angle identities, giving $\cos 2\theta$ and $\sin 2\theta$ in place of $\cos\theta$ and $\sin\theta$ .

2023: 30 May Shift 3

Let $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3 \end{bmatrix}$ . If $A^{-1}$ does not exist, then $\lambda =$

2026: 22 May Shift 1

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

Match List-I with List-II

List-I	List-II
(A) $\left\vert A \right\vert =$	(I) $\dfrac{1}{9}$
(B) $\left\vert A^{-1} \right\vert =$	(II) $81$
(C) $\left\vert \text{adj } A \right\vert =$	(III) $9$
(D) $\left\vert \text{adj } (\text{adj } A) \right\vert =$	(IV) $6561$

Choose the correct answer from the options given below:

2026: 12 May Shift 2

If $\begin{vmatrix}4x & 9\\ -4 & -5\end{vmatrix}=\begin{vmatrix}4 & 8\\ 2 & 3\end{vmatrix}$ , then the value of $x$ is :

2026: 22 May Shift 2

If $A=\begin{bmatrix}k & 2\\2 & k\end{bmatrix}$ such that $\lvert A^3 \rvert = 125$ then which of the following statements are TRUE?

(A) $\lvert k.adj(3A) \rvert = 405$

(B) $\lvert k.adj(3A) \rvert = 2025$

(D) $\lvert adj(3A) \rvert = 45$

Choose the correct answer from the options given below:

2025: 3 June Shift 2

Which of the following statement is/are correct?

(A) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij} = a_{ji}$ for all $i, j$

(B) $A = [a_{ij}]_{m \times m}$ is a diagonal matrix if $a_{ij} = 0$ when $i = j$

(D) The multiplication of diagonal matrices of same order is commutative

Choose the correct answer from the options given below:

2026: 31 May Shift 2

If $A = \begin{bmatrix} 2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4 \end{bmatrix}$ , then $A^2$ is equal to :

If the matrix A=[cos⁡θsin⁡θ−sin⁡θcos⁡θ]A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}A=[cosθ−sinθ​sinθcosθ​], then A2A^2A2 is equal to:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If the matrix $A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$ , then $A^2$ is equal to: