Question

Find the inverse of the following matrix :
(i)$\left[\begin{array}{cc}1& 2\\ 2& -1\end{array}\right]$

Answer 1

The inverse of Matrix is defined as $\frac{Adj\left(A\right)}{Det\left(A\right)}$

$adj\left(A\right)$ is given as $\left[\begin{array}{ccc}-1& & -2\\ -2& & 1\end{array}\right]$

$Det\left(A\right)=-1-4=-5$

So the inverse of matrix is $-\frac{1}{5}$ $\left[\begin{array}{ccc}-1& & -2\\ -2& & 1\end{array}\right]$