If A=bmatrix3 & -2\\4 & -2bmatrix and I=bmatrix1 & 0\\0 & 1bmatrix such that A^2-A+ I=0, then value of '' is: Option 1: 1 Option 2: -1 Option 3: 2 Option 4: -2

Answer: 2. Solution: A^2=bmatrix1&-2\\4&-4bmatrix, so A^2-A=bmatrix-2&0\\0&-2bmatrix=-2I. Then -2I+ I=O gives =2.

Algebra

Matrices & Determinants

Easy

core

If $A=\begin{bmatrix}3 & -2\\4 & -2\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ such that $A^2-A+\lambda I=0$ , then value of ' $\lambda$ ' is:

-1

-2

✅ Correct Option: 3

$A^2=\begin{bmatrix}1&-2\\4&-4\end{bmatrix}$ , so $A^2-A=\begin{bmatrix}-2&0\\0&-2\end{bmatrix}=-2I$ .

Then $-2I+\lambda I=O$ gives $\lambda=2$ .

2025: 2 June Shift 1

If $A$ is an invertible matrix of order 3, then

Match List-I with List-II

List-I	List-II
(A) $\vert \text{adj} A\vert$	(I) $8\vert A\vert$
(B) $\vert A(\text{adj} A)\vert$	(II) $\vert A\vert ^2$
(C) $\vert 2A\vert$	(III) $\frac{1}{\vert A\vert }$
(D) $\vert A^{-1}\vert$	(IV) $\vert A\vert ^3$

Choose the correct answer from the options given below:

2025: 19 May Shift 1

If $A = \begin{bmatrix} 2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0 \end{bmatrix}$ , then the value of det (adj (2A)) is:

2024: 16 May Shift 1

If $A$ is a square matrix and $I$ is an identity matrix such that $A^{2}=A$ , then $A(I-2 A)^{3}+2 A^{3}$ is equal to :

2025: 30 May Shift 2

Let $A$ and $B$ be square matrices of order 3, then det $[(A - A^T) + (B - B^T)]$ is equal to

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
A is given matrix	$\left\vert \text{adj}(\text{adj}A) \right\vert$
(A) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 3$	(I) $3$
(B) Order of A $= 3 \times 3$ and $\left\vert A \right\vert = 2$	(II) $1$
(C) Order of A $= 4 \times 4$ and $\left\vert A \right\vert = 1$	(III) $16$
(D) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 4$	(IV) $4$

Choose the correct answer from the options given below:

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:

If A=[3−24−2]A=\begin{bmatrix}3 & -2\\4 & -2\end{bmatrix}A=[34​−2−2​] and I=[1001]I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}I=[10​01​] such that A2−A+λI=0A^2-A+\lambda I=0A2−A+λI=0, then value of 'λ\lambdaλ' is:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If $A=\begin{bmatrix}3 & -2\\4 & -2\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ such that $A^2-A+\lambda I=0$ , then value of ' $\lambda$ ' is: