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CUET · MATHS · PYQ PAPER 2023

If \(A=\left[\begin{array}{cc}3 & 1 \\ 2 & -3\end{array}\right]\) be such that \(A^{-1}=K A\), then the value of \(K\) is :

  1. A 11
  2. B \(-11\)
  3. C \(\frac{1}{11}\)
  4. D \(-\frac{1}{11}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{11}\)

Step-by-step Solution

Detailed explanation

\(\det(A) = (3)(-3) - (1)(2) = -9 - 2 = -11\) \(A^{-1} = \frac{1}{\det(A)} \text{adj}(A) = \frac{1}{-11} \left[\begin{array}{cc}-3 & -1 \\ -2 & 3\end{array}\right] = \left[\begin{array}{cc}\frac{3}{11} & \frac{1}{11} \\ \frac{2}{11} & -\frac{3}{11}\end{array}\right]\)…