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CUET · MATHS · PYQ PAPER 2025

Which of the following are correct?
(A) For a square matrix \(A\), if \(A^3=I\), then \(A^{-1}=A^2\).
(B) The determinant of only a square matrix can be defined.
(C) If \(A\) is a square matrix of order 3 , then the number of minors of the matrix \(A\) is 3 .
(D) If \(A\) and \(B\) are two non-singular matrices of the same order, then \((A B)^{-1}=B^{-1} A^{-1}\).
Choose the correct answer from the options given below :

  1. A (A), (B) and (D) only
  2. B (A), (B) and (C) only
  3. C (B) and (D) only
  4. D (C) and (D) only
Verified Solution

Answer & Solution

Correct Answer

(A) (A), (B) and (D) only

Step-by-step Solution

Detailed explanation

Statement (A): \(A^3=I \implies A^{-1}A^3 = A^{-1}I \implies A^2=A^{-1}\). Correct. Statement (B): Determinants are defined only for square matrices. Correct. Statement (C): For a matrix of order 3, there are \(3^2=9\) minors. Incorrect. Statement (D): The inverse of a product…
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