Inverse matrix

An inverse matrix, or inverse of a matrix, is a non-singular square matrix that produces the identity matrix when multiplied by or to its corresponding inverse. For a given matrix <math>A\in\mathcal{M}_{n\times n}</math>, the inverse exists if and only if the determinant of <math>A</math> is non-zero, <math>\det A \neq 0</math>. Such a matrix is called a non-singular matrix. The inversion of a matrix is itself invertible, i.e. <math>(A^{-1})^{-1} = A</math>

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>.

However, this formula does not hold for matrices larger than 2x2.