Question

Determine, caso exista, a matriz inversa de A= $\left[\begin{array}{ccc}2&0&\\4&-3\\\end{array}\right]$

Answer 1

$\boxed{\begin{array}{l}\sf A=\begin{bmatrix}\sf2&\sf0\\\sf4&\sf-3\end{bmatrix}\\\sf det~A=2\cdot(-3)-4\cdot0=-6\\\\\sf cof~A=\begin{bmatrix}\sf-3&\sf-4\\\sf0&\sf2\end{bmatrix}\\\\\sf Adj~A=(cof~A)^T\\\sf Adj~A=\begin{bmatrix}\sf-3&\sf0\\\sf-4&\sf2\end{bmatrix}\\\sf A^{-1}=\dfrac{1}{det~A}\cdot Adj~A\\\\\sf A^{-1}=-\dfrac{1}{6}\cdot\begin{bmatrix}\sf-3&\sf0\\\sf-4&\sf2\end{bmatrix}\\\\\sf A^{-1}=\begin{bmatrix}\sf\dfrac{1}{2}&\sf0\\\\\sf\dfrac{2}{3}&\sf-\dfrac{1}{3}\end{bmatrix}\end{array}}$