CUET · MATHS · PYQ PAPER 2025
If \(A\) and \(B\) are square matrices of the same order, then which of the following statements are correct?
(A) \(\left|A^{-1}\right|=|A|^{-1}\)
(B) \(\operatorname{adj}(A)=|A| A^{-1}\)
(C) \((A+B)^{-1}=B^{-1}+A^{-1}\)
(D) \((A B)^{-1}=B^{-1} A^{-1}\)
Choose the correct answer from the options given below :
- A (A), (B) and (D) only
- B (A), (B) and (C) only
- C (A), (C) and (D) only
- D (B), (C) and (D) only
Answer & Solution
Correct Answer
(A) (A), (B) and (D) only
Step-by-step Solution
Detailed explanation
Statements (A), (B), and (D) are correct properties of matrices. (A) \( \left|A^{-1}\right|=|A|^{-1} \) (B) \( \operatorname{adj}(A)=|A| A^{-1} \) (C) \( (A+B)^{-1} \neq B^{-1}+A^{-1} \) (D) \( (A B)^{-1}=B^{-1} A^{-1} \) The correct option is (A), (B) and (D) only.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- If \(y=500 e^{7 x}+600 e^{-7 x}\), then \(\frac{d^2 y}{d x^2}\) is equal to :CUET 2023 Easy
- If \(A=\left[a_{i j}\right]\) is a square matrix of order 2 such that, \(a_{i j}=\left\{\begin{array}{ll}2, & \text { when } i \neq j \\ 0, & \text { when } i=j\end{array}\right.\), then \(\operatorname{det}\left(A^2\right)\) is:CUET 2025 Easy
- A cell of emf 1.1 V and internal resistance \(0.5 \Omega\) is connected to a \(0.5 \Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :CUET 2024 Hard
- Let \(A =\left[a_{i j}\right]\) be a \(2 \times 2\) matrix such that \(a_{i j}=\frac{|-3 i+j|}{2}\) then \(a_{21}\) is :CUET 2023 Easy
- A spherical ice ball is melting at the rate of \(100 \pi \mathrm{~cm}^3 / \mathrm{min}\). The rate at which its radius is decreasing when its radius is 15 cm, isCUET 2025 Easy
- The domain of the function \(y=\sin ^{-1}(x-1)+\cos ^{-1} \sqrt{x-1}\) is:CUET 2025 Medium
More PYQs from CUET
- If primary producers are exposed to 1,000,000 Joules of sunlight, the amount of energy transferred to tertiary consumers will be:CUET 2025 Medium
- Identify the contraceptive measure which can not be practiced by human females:CUET 2023 Hard
- Two long straight parallel wires are carrying charges \( \lambda_1 \) and \( \lambda_2 \) per unit length, respectively. The separation between their axes is d. The magnitude of the force exerted on unit length of one wire due to the charge on the other wire isCUET 2025 Hard
- The molecule with largest \(C-X\) bond length isCUET 2023 Medium
- Number of unpaired electrons in the square planar [Pt(CN)4]2- are :CUET 2025 Hard
- Match List-I with List-II
Choose the correct answer from the options given below :List-I ( Matrix A ) List-II ( Determinant of adj A ) (A) \(\left[\begin{array}{cc}2 & 1 \\0 & -1\end{array}\right]\) (I) 6 (B) \(\left[\begin{array}{cc}0 & 1 \\4 & -1\end{array}\right]\) (II) 5 (C) \(\left[\begin{array}{cc}1 & 2 \\-3 & -1\end{array}\right]\) (III) \(-4\) (D) \(\left[\begin{array}{cc}4 & -2 \\3 & 0\end{array}\right]\) (IV) \(-2\) CUET 2025 Easy