[Tex/LaTex] Inverse Matrix of A

Question

I would like to know how to write an inverse matrix off A. I have tried everything i could think off but i had no success. Could anybody give me a simple 2×2 example(I don´t know how to get -1 over the matrix bracket). Thank you

Answer 1

Something like this?

\documentclass{article}
\usepackage{mathtools} % for 'bmatrix*' env.; loads 'amsmath' package automatically
\begin{document}
Let
\[
A = \begin{bmatrix}
       a_{11} & a_{12} \\ 
       a_{21} & a_{22}
    \end{bmatrix}
\]
be a full-rank $2\times2$ matrix. 
Then $\det A\equiv\lvert A\rvert=a_{11}a_{22}-a_{12}a_{21}\ne0$ and 
\[
A^{-1}=\begin{bmatrix}
          a_{11} & a_{12} \\ 
          a_{21} & a_{22}
       \end{bmatrix}^{-1}
      =\frac{1}{\lvert A\rvert}
       \begin{bmatrix*}[r]
           a_{22} & -a_{12} \\ 
          -a_{21} &  a_{11}
       \end{bmatrix*} \,.
\]
\end{document}