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 :
- A 11
- B \(-11\)
- C \(\frac{1}{11}\)
- D \(-\frac{1}{11}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{11}\)
Step-by-step Solution
Detailed explanation
\(\det(A) = (3)(-3) - (1)(2) = -9 - 2 = -11\) \(A^{-1} = \frac{1}{\det(A)} \text{adj}(A) = \frac{1}{-11} \left[\begin{array}{cc}-3 & -1 \\ -2 & 3\end{array}\right] = \left[\begin{array}{cc}\frac{3}{11} & \frac{1}{11} \\ \frac{2}{11} & -\frac{3}{11}\end{array}\right]\)…
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