# Inverse Matrix Another method?

Is there another method (involving determinants) for finding the inverse of a matrix than making the matrix equal to what it is supposed to look like in reduced row echelon form? Please explain. Thanks

## 2 Answers

Inverse of matrix (suppose A)

$$A^{-1} =\frac{ adjoint(A)}{det(A)}$$

*$A^{-1}$ Exist iff $det(A)≠0$

For a $(2\times2)$-matrix you may use the following formula:

$$\frac{1}{ad-bc}\cdot \begin{pmatrix} d & -b \\ -c & a \\ \end{pmatrix}.$$