Inverse Matrix
Inverse Matrixes are basically Linear Transformations that can reverse the effects of a matrix. Finding the inverse of a matrix is done through this method:
- An augmented matrix of type $\begin{bmatrix} A & | & I_n \end{bmatrix}$, where $I_n$ is an identity matrix of size $n \times n$.
- If $A$ is invertible, than you can use Elementary Row Operations in order to reduce the augmented matrix so that it is in the form $\begin{bmatrix} I_n & | & A^{-1} \end{bmatrix}$