MHT CET · Maths · Matrices
If \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 3 & 1\end{array}\right]\), then \((A B)^{-1}=\)
- A \(\left[\begin{array}{cc}2 & -3 \\ -7 & 11\end{array}\right]\)
- B \(\left[\begin{array}{cc}2 & -3 \\ 7 & 11\end{array}\right]\)
- C \(\left[\begin{array}{cc}2 & -3 \\ -7 & -11\end{array}\right]\)
- D \(\left[\begin{array}{cc}-2 & -3 \\ -7 & 11\end{array}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\begin{array}{cc}2 & -3 \\ -7 & 11\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\(A B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 3 & 1\end{array}\right]=\left[\begin{array}{cc}11 & 3 \\ 7 & 2\end{array}\right]\) \(\Rightarrow|A B|=\left|\begin{array}{cc}11 & 3 \\ 7 & 2\end{array}\right|=22-21=1\)
\(\operatorname{adj}(A B)=\left[\begin{array}{cc}2 & -3 \\ -7 & 11\end{array}\right] \Rightarrow(A B)^{-1}=\left[\begin{array}{cc}2 & -3 \\ -7 & 11\end{array}\right]\)
\(\operatorname{adj}(A B)=\left[\begin{array}{cc}2 & -3 \\ -7 & 11\end{array}\right] \Rightarrow(A B)^{-1}=\left[\begin{array}{cc}2 & -3 \\ -7 & 11\end{array}\right]\)
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