First, let me show you some notation.
To show a matrix is an inverse of another matrix, we write [tex]A^{-1}[/tex]
-1 is not an exponent. It just shows that a matrix is an inverse of another matrix.
For a 2x2 matrix, we can get the inverse by first making b and c negatives and swap the positions of a and d.
Then multiply each entry in the matrix by 1 divided by the determinant.
[tex] \left[\begin{array}{ccc}a&b\\c&d\end{array}\right]^{-1} =
\frac{1}{ad - bc}\left[\begin{array}{ccc}d&{-b}\\{-c}&a\end{array}\right] = \\ \\ \\ \left[\begin{array}{ccc}d(\frac{1}{ad-bc})&{-b}(\frac{1}{ad-bc}) \\ {-c}(\frac{1}{ad-bc}) &a(\frac{1}{ad-bc}) \end{array}\right][/tex]
I hope this helped!
