Question

Determine a Matriz inversa da transposta da matriz M

Answer 1

$\large\boxed{\begin{array}{l}\sf M=\begin{pmatrix}\sf-1&\sf-2\\\sf2&\sf1\end{pmatrix}\\\sf det~M=-1\cdot1+2\cdot2=-1+4=3\\\sf cof~M=\begin{pmatrix}\sf1&\sf-2\\\sf2&\sf-1\end{pmatrix}\\\sf adj~M=\begin{pmatrix}1&\sf2\\\sf-2&\sf-1\end{pmatrix}\\\sf M^{-1}=\dfrac{1}{det~M}\cdot adj~M\\\sf M^{-1}=\dfrac{1}{3}\cdot\begin{pmatrix}\sf1&\sf2\\\sf-2&\sf-1\end{pmatrix} \\ \\\sf M^{-1}=\begin{pmatrix}\dfrac{1}{3}&\sf\dfrac{2}{3}\\ \\\sf-\dfrac{2}{3}&\sf-\dfrac{1}{3}\end{pmatrix} \\ \\\sf (M^{-1})^T=\begin{pmatrix}\dfrac{1}{3}&\sf-\dfrac{2}{3} \\ \\\sf\dfrac{2}{3}&\sf-\dfrac{1}{3}\end{pmatrix} \end{array}}$