KCET · Maths · Matrices
If \(\left(\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right) A=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\), then the matrix \(a\) is
- A \(\left(\begin{array}{cc}2 & 1 \\ 3 & 2\end{array}\right)\)
- B \(\left(\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right)\)
- C \(\left(\begin{array}{cc}-2 & 1 \\ 3 & -2\end{array}\right)\)
- D \(\left(\begin{array}{cc}2 & -1 \\ 3 & 2\end{array}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right)\)
Step-by-step Solution
Detailed explanation
We have,
\(\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)
Let
\(B=\left[\begin{array}{ll}
2 & 1 \\
3 & 2
\end{array}\right]\)
\(\therefore \quad B A=I\)
\(A=B^{-1} I\)
\(A=B^{-1}\)
\(\therefore \quad B^{-1}=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]\)
Hence, \(A=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]\)
\(\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)
Let
\(B=\left[\begin{array}{ll}
2 & 1 \\
3 & 2
\end{array}\right]\)
\(\therefore \quad B A=I\)
\(A=B^{-1} I\)
\(A=B^{-1}\)
\(\therefore \quad B^{-1}=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]\)
Hence, \(A=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]\)
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