Inverse matrix

An inverse matrix, or inverse of a matrix, is the square matrix that produces the identity matrix when multiplied by its corresponding inverse. For a given matrix <math>A</math> the inverse exists if and only if the determinant of <math>A</math> is non-zero, <math>\det A \neq 0</math>. The inverse of an inverse is the original matrix.

The formula for finding the inverse of a 2x2 matrix is as follows:

<math>A = \begin{pmatrix}a & b \\ c & d\end{pmatrix} \Rightarrow A^{-1} = \frac{1}{ad - bc}\begin{pmatrix} d & -b \\ -c & a\end{pmatrix} </math>.