CUET · MATHS · PYQ PAPER 2023
The inverse of the matrix \(\left[\begin{array}{cc}5 & 11 \\ 1 & 2\end{array}\right]\) is:
- A \(\left[\begin{array}{cc}-2 & 11 \\ 1 & -5\end{array}\right]\)
- B \(\left[\begin{array}{cc}2 & -11 \\ -1 & 5\end{array}\right]\)
- C \(\left[\begin{array}{cc}5 & 1 \\ 11 & 2\end{array}\right]\)
- D \(\left[\begin{array}{cc}5 & -1 \\ -11 & 2\end{array}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\begin{array}{cc}-2 & 11 \\ 1 & -5\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\(\det(A) = (5)(2) - (11)(1) = 10 - 11 = -1\) \(A^{-1} = \frac{1}{-1}\left[\begin{array}{cc}2 & -11 \\ -1 & 5\end{array}\right] = \left[\begin{array}{cc}-2 & 11 \\ 1 & -5\end{array}\right]\)
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