Question

Determine a inversa da matriz:

P= [ 1 1]
[ 1 -1]

Answer 1

 Por escalonamento,

$\begin{bmatrix}1&1&|1&0\\1&-1&|0&1&\end{bmatrix}=\\\\L_2\rightarrow\,L_1-L_2\\\\\begin{bmatrix}1&1&|1&0\\0&2&|1&-1&\end{bmatrix}=\\\\L_2\rightarrow\,\frac{L_2}{2}\\\\\begin{bmatrix}1&1&|1&0\\0&1&|\frac{1}{2}&\frac{-1}{2}&\end{bmatrix}=\\\\L_1\rightarrow\,L_1-L_2\\\\\\\begin{bmatrix}1&0&|\frac{1}{2}&\frac{1}{2}\\0&1&|\frac{1}{2}&\frac{-1}{2}&\end{bmatrix}$
  
 Logo, $\boxed{\boxed{\begin{bmatrix}\frac{1}{2}&\frac{1}{2}\\\\\frac{1}{2}&-\frac{1}{2}&\end{bmatrix}}}$.