# How do you find the inverse of A=((-7, 33), (4, -19))?

Mar 11, 2016

${A}^{- 1} = \left[\begin{matrix}19 & - 33 \\ - 4 & - 7\end{matrix}\right]$

#### Explanation:

${A}^{- 1} = \frac{1}{\det \left(A\right)} \cdot a \mathrm{dj} \left(A\right)$

$= \frac{1}{\left(- 7 \times - 19\right) - \left(33 \times 4\right)} \cdot \left[\begin{matrix}- 19 & - 33 \\ - 4 & - 7\end{matrix}\right]$

$= \left[\begin{matrix}19 & - 33 \\ - 4 & - 7\end{matrix}\right]$.

An alternative method would be to augment the given matrix A with the $2 \times 2$ identity matrix ${I}_{2}$ and then perform Gaussian elementary row operations to obtain the identity matrix on the left hand side, then what's left on the right hand side will be the inverse of A. This method would take longer though but would still culminate in the same final answer.