Question

Find the inverse of the matrix-
$\left[\begin{array}{cc}3& -2\\ -1& 1\end{array}\right]$

Answer 1

Let $A=\left[\begin{array}{cc}3& -2\\ -1& 1\end{array}\right]$

Inverse of matrix is given as

$A^{-1}=\frac{AdjA}{DetA}$

Adj $A=$$\left[\begin{array}{cc}1& 2\\ 1& 3\end{array}\right]$

$|A|=3\left(1\right)-(-2)(-1)=3-2=1$

So Inverse of matrix is

$A^{-1}=\frac{\left[\begin{array}{cc}1& 2\\ 1& 3\end{array}\right]}{1}=\left[\begin{array}{cc}1& 2\\ 1& 3\end{array}\right]$