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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.

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:

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>.

<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>.

 

[[Category:linear algebra]]

[[Category:linear algebra]]