What is $A^{-1}$ for $A = \begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix}$?

Explanation

1. 01

   $|A| = 8 - 3 = 5$, which is not 0, so the inverse exists.

2. 02

   $\operatorname{adj} A = \begin{bmatrix}4 & -3 \\ -1 & 2\end{bmatrix}$, and $A^{-1} = \frac{1}{5}\operatorname{adj} A = \begin{bmatrix}\frac{4}{5} & - \frac{3}{5} \\ - \frac{1}{5} & \frac{2}{5}\end{bmatrix}$.