If P = 1/14bmatrix 3 & 2 \\ -4 & 2 bmatrix and P^(-1) = bmatrix x & -2 \\ 4 & y bmatrix, then the value of x and y respectively are Option 1: -3 and -2 Option 2: -2 and 3 Option 3: 3 and 2 Option 4: 2 and 3

Answer: 2 and 3. Solution: P, =1/14^2(3* 2-2(-4))=14/196=1/14. P^(-1)=141/14bmatrix2&-2\\4&3bmatrix=bmatrix2&-2\\4&3bmatrix. Comparing, x=2, y=3.

Algebra

Matrices & Determinants

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If $P = \dfrac{1}{14}\begin{bmatrix} 3 & 2 \\ -4 & 2 \end{bmatrix}$ and $P^{-1} = \begin{bmatrix} x & -2 \\ 4 & y \end{bmatrix}$ , then the value of $x$ and $y$ respectively are

-3 and -2

-2 and 3

3 and 2

2 and 3

✅ Correct Option: 4

$|P|=\dfrac{1}{14^2}(3\cdot 2-2\cdot(-4))=\dfrac{14}{196}=\dfrac{1}{14}$ .

$P^{-1}=14\cdot\dfrac{1}{14}\begin{bmatrix}2&-2\\4&3\end{bmatrix}=\begin{bmatrix}2&-2\\4&3\end{bmatrix}$ .

Comparing, $x=2$ , $y=3$ .

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If A is a square matrix and I is an identity matrix of same order such that $A^2 = A$ , then $(I + A)^3 - 8I$ is equal to

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Match List-I with List-II

List-I	List-II
Type of matrix	Conditions
(A) Square matrix A	(I) $A = [a_{ij}]_{m \times m}$ where $\begin{cases} a_{ij} = 0 & , i \neq j \\ a_{ij} = k & , i = j \end{cases}$ , where $k \neq 0$ is constant.
(B) Scalar Matrix A	(II) $A = [a_{ij}]_{m \times m}$
(C) Diagonal matrix A	(III) $A = [a_{ij}]_{m \times m}$ where $\begin{cases} a_{ij} = 0 & , i \neq j \\ a_{ij} = 1 & , i = j \end{cases}$
(D) Identity matrix A	(IV) $A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0$ , $i \neq j$

Choose the correct answer from the options given below:

2026: 18 May Shift 1

Let $A$ and $B$ be two symmetric matrices of same order, then

Match List-I with List-II

List-I	List-II
(A). $AB - BA$	(I). Neither symmetric nor Skew symmetric
(B). $BA - 2AB$	(II). Skew symmetric
(C). $AB + BA$	(III). Null matrix
(D). $(AB)^T - BA$	(IV). Symmetric

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 :

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If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$ , then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)

2026: 22 May Shift 1

If $A=\begin{bmatrix}\lambda & 0 & 0\\0 & \lambda & 0\\0 & 0 & \lambda\end{bmatrix}$ , $\lambda\ne0$ , then $|adjA|$ is equal to

If P=114[32−42]P = \dfrac{1}{14}\begin{bmatrix} 3 & 2 \\ -4 & 2 \end{bmatrix}P=141​[3−4​22​] and P−1=[x−24y]P^{-1} = \begin{bmatrix} x & -2 \\ 4 & y \end{bmatrix}P−1=[x4​−2y​], then the value of xxx and yyy respectively are

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $P = \dfrac{1}{14}\begin{bmatrix} 3 & 2 \\ -4 & 2 \end{bmatrix}$ and $P^{-1} = \begin{bmatrix} x & -2 \\ 4 & y \end{bmatrix}$ , then the value of $x$ and $y$ respectively are