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 $A$ the inverse exists if and only if the determinant of $A$ is non-zero, $\det A\neq 0$. The inverse of an inverse is the original matrix.

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

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