Question

Calcule a inversa da matriz A=(2 3)
(3 5)

Answer 1

$\large\boxed{\begin{array}{l}\rm A=\begin{pmatrix}\rm2&\rm3\\\rm3&\rm5\end{pmatrix}\\\rm det\,A=2\cdot5-3\cdot3\\\rm det\,A=10-9\\\rm det\,A=1\longrightarrow matriz\,invers\acute ivel\\\rm cof\,A=\begin{pmatrix}\rm5&\rm-3\\\rm-3&\rm2\end{pmatrix}\\\\\rm adj\,A=cof A^T\\\rm adj\,A=\begin{pmatrix}\rm5&\rm-3\\\rm-3&\rm2\end{pmatrix}\\\\\rm A^{-1}=\dfrac{1}{det\,A}\cdot Adj\,A\\\\\rm A^{-1}=\dfrac{1}{1}\cdot\begin{pmatrix}\rm5&\rm-3\\\rm-3&\rm2\end{pmatrix} \end{array}}$

$\Huge\boxed{\begin{array}{l}\rm A^{-1}=\begin{pmatrix}~~\rm5&\rm-3\\\rm-3&~~\rm2\end{pmatrix}\end{array}}$