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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
Question
Find the inverse of the matrix $\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$
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Answer

Let $A=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$
$\therefore| A |=\left|\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right|=4-3=1 \neq 0  $
$ \therefore A ^{-1} \text { exists. }  $
$ \therefore AA ^{-1}= I  $
$ {\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right] A^{-1}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]}  $
$ R _1 \rightarrow R _1+ R _2 $
$ {\left[\begin{array}{cc}1 & -1 \\ -1 & 2\end{array}\right] A^{-1}=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]}  $
$ R _2 \rightarrow R _2+ R _1 $
$ {\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right] A^{-1}=\left[\begin{array}{ll}1 & 1 \\ 1 & 2\end{array}\right]}  $
$ R_1 \rightarrow R_1+R_2  $
${\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] A^{-1}=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]}  $
$ \therefore A ^{-1}=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right] $

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