Search any question & find its solution
Question:
Answered & Verified by Expert
The inverse of $\left[\begin{array}{cc}2 & -3 \\ -4 & 2\end{array}\right]$ is
Options:
Solution:
2696 Upvotes
Verified Answer
The correct answer is:
$\frac{-1}{8}\left[\begin{array}{ll}2 & 3 \\ 4 & 2\end{array}\right]$
Let $A=\left[\begin{array}{cc}2 & -3 \\ -4 & 2\end{array}\right], \left.\quad \therefore A|=| \begin{array}{cc}2 & -3 \\ -4 & 2\end{array} \right\rvert\,=4-12=-8$
The matrix of cofactors of the elements of $A$ viz.
$\left[\begin{array}{ll}c_{11} & c_{12} \\ c_{21} & c_{22}\end{array}\right]=\left[\begin{array}{cc}2 & -(-4) \\ -(-3) & 2\end{array}\right]=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$
$\therefore \operatorname{adj} A=$ transpose of the matrix of cofacters
of elements of $A=\left[\begin{array}{ll}2 & 3 \\ 4 & 2\end{array}\right]$
The matrix of cofactors of the elements of $A$ viz.
$\left[\begin{array}{ll}c_{11} & c_{12} \\ c_{21} & c_{22}\end{array}\right]=\left[\begin{array}{cc}2 & -(-4) \\ -(-3) & 2\end{array}\right]=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$
$\therefore \operatorname{adj} A=$ transpose of the matrix of cofacters
of elements of $A=\left[\begin{array}{ll}2 & 3 \\ 4 & 2\end{array}\right]$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.