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CUET · MATHS · PYQ PAPER 2023

If \(A\) and \(B\) are invertible matrices of the same order, then which of the following statements is not true?

  1. A \(\left|A^{-1}\right|=|A|^{-1}\)
  2. B \(|A| A^{-1}=\operatorname{Adj} A\)
  3. C \((A+B)^{-1}=B^{-1}+A^{-1}\)
  4. D \((A B)^{-1}=B^{-1} A^{-1}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((A+B)^{-1}=B^{-1}+A^{-1}\)

Step-by-step Solution

Detailed explanation

A) \(\left|A^{-1}\right|=|A|^{-1}\) (True): The determinant of an inverse matrix is equal to the reciprocal of the determinant of the original matrix. B) \(|A| A^{-1}=\operatorname{Adj} A\) (True): This is derived from the standard formula for the inverse of a matrix:…