Algebra

Matrices & Determinants

Medium

common

If $A$ is a square matrix such that $|A| \neq 0$ and $A^2 - A + 2I = 0$ then $A^{-1}$ is equal to :(where $I$ is an identity matrix of order as order of matrix $A$ )

$\dfrac{1}{2}(I - A)$

$I + A$

$I - A$

$\dfrac{1}{2}(I + A)$

✅ Correct Option: 1

From $A^2-A+2I=0$ we get $2I=A-A^2=A(I-A)$ . Multiplying both sides by $A^{-1}$ gives $2A^{-1}=I-A$ , so $A^{-1}=\frac{1}{2}(I-A)$ .

2025: 16 May Shift 1

Match List-I with List-II

Let $A$ be any invertible square matrix. Then

List-I	List-II
(A) $A - A^T$	(I) $\vert A\vert A^{-1}$
(B) $A A^T$	(II) Skew-symmetric
(C) $\det (A^{-1})$	(III) Symmetric
(D) $\text{adj} A$	(IV) $[\det(A)]^{-1}$

Choose the correct answer from the options given below:

2023: 30 May Shift 3

Given $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} x & y \\ 1 & 4 \end{bmatrix}$ , If $A = B$ , then $x$ and $y$ are :

2026: 19 May Shift 2

If $\begin{vmatrix} 1+x^2 & 1 & 1 \\ 1 & 1+y^2 & 1 \\ 1 & 1 & 1+z^2 \end{vmatrix} = k\left(1 + \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}\right)$ then $k$ is equal to

2026: 31 May Shift 2

If A is a square matrix of order $n$ and $k$ is a scalar such that $|kA| = \alpha|A|$ then the value of $\alpha$ is:

2025: 30 May Shift 2

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

2026: 15 May Shift 1

If $A$ is a square matrix of order 3 such that $|A|=3$ , then the value of $|adj(adjA)|$ is equal to

If AAA is a square matrix such that ∣A∣≠0|A| \neq 0∣A∣=0 and A2−A+2I=0A^2 - A + 2I = 0A2−A+2I=0 then A−1A^{-1}A−1 is equal to :(where III is an identity matrix of order as order of matrix AAA)

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A$ is a square matrix such that $|A| \neq 0$ and $A^2 - A + 2I = 0$ then $A^{-1}$ is equal to :(where $I$ is an identity matrix of order as order of matrix $A$ )