CUET · MATHS · PYQ PAPER 2023
If \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -2 \\ 1 & 3\end{array}\right]\), then which of the following are incorrect?
(A) \(|A|=5\)
(B) \(\operatorname{Adj} A=\left[\begin{array}{ll}4 & 3 \\ 1 & 2\end{array}\right]\)
(C) \(A(\operatorname{Adj} A)=25 I\)
(D) \(|3 B|=45\)
(E) \((A B)^{-1}=B^{-1} A^{-1}\)
Choose the correct answer from the options given below:
- A \(B, C\) only
- B \(B, C, D\) only
- C \(A, B\) only
- D \(A, B, E\) only
Answer & Solution
Correct Answer
(A) \(B, C\) only
Step-by-step Solution
Detailed explanation
\(|A| = 2(4) - 3(1) = 5\) \(\operatorname{Adj} A=\left[\begin{array}{cc}4 & -3 \\ -1 & 2\end{array}\right]\) \(A(\operatorname{Adj} A)=|A| I = 5 I\) \(|B| = 1(3) - (-2)(1) = 5\) \(|3 B|=3^2 |B| = 9(5) = 45\) \((A B)^{-1}=B^{-1} A^{-1}\) is true by property. Statements (B) and…
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