If A = bmatrix x & 1 \\ y & -1 bmatrix, B = bmatrix 1 & -1 \\ 2 & -1 bmatrix and (A+B)^2 = A^2 + B^2, then Option 1: x = -4, y = 1 Option 2: x = 4, y = 1 Option 3: x = 1, y = 4 Option 4: x = -1, y = 4

Answer: x = 1, y = 4. Solution: Since (A+B)^2=A^2+AB+BA+B^2, the condition reduces to AB+BA=O. Computing gives AB+BA=bmatrix2x+2-y & 1-x\\ 2x-2 & 4-ybmatrix. Equating each entry to zero yields x=1 from 1-x=0 and y=4 from 4-y=0, which also satisfy the remaining entries.

Algebra

Matrices & Determinants

Medium

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If $A = \begin{bmatrix} x & 1 \\ y & -1 \end{bmatrix}, B = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$ , then

$x = -4, y = 1$

$x = 4, y = 1$

$x = 1, y = 4$

$x = -1, y = 4$

✅ Correct Option: 3

Since $(A+B)^2=A^2+AB+BA+B^2$ , the condition reduces to $AB+BA=O$ . Computing gives $AB+BA=\begin{bmatrix}2x+2-y & 1-x\\ 2x-2 & 4-y\end{bmatrix}$ . Equating each entry to zero yields $x=1$ from $1-x=0$ and $y=4$ from $4-y=0$ , which also satisfy the remaining entries.

2025: 14 May Shift 2

The values of $\lambda$ for which the system of equation $x + 2y + z = 14, - x + y + z = 10, x + \lambda y + z = 2$ has unique solution is

2025: 30 May Shift 2

If A is a singular matrix, then A{adj A} is equal to

2026: 31 May Shift 2

For any non-zero matrix $A = [a_{ij}]_{3\times3}$ and $|A| \neq 0$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert adj\,A \vert$	I.	$\dfrac{1}{\vert A \vert}(adj\,A)$
B.	$(adj\,A)A$	II.	$\vert A \vert^2$
C.	$A^{-1}$	III.	$\dfrac{1}{\vert A \vert}$
D.	$\vert A^{-1} \vert$	IV.	$\vert A \vert I$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

If $A = \begin{bmatrix} -2 & 6 \\ -5 & -1 \end{bmatrix}$ then $A^{-1}$ is :

2025: 13 May Shift 1

If $A = [a_{ij}]_{2×2}$ where $a_{ij} = \begin{cases} 1, & i \neq j \\ 0, & i = j \end{cases}$ and $I$ is the identity matrix of order 2, then $(A^2 - 3A + 4I)$ is

(A) Symmetric Matrix

(B) Skew-symmetric Matrix

(D) Square Matrix

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=[x1y−1],B=[1−12−1]A = \begin{bmatrix} x & 1 \\ y & -1 \end{bmatrix}, B = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}A=[xy​1−1​],B=[12​−1−1​] and (A+B)2=A2+B2(A+B)^2 = A^2 + B^2(A+B)2=A2+B2, then

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} x & 1 \\ y & -1 \end{bmatrix}, B = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$ , then