# Matrix Inversion Operation

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A Matrix Inversion Operation is a unary matrix operation that creates matrix [math]\displaystyle{ A^{-1} }[/math] such that [math]\displaystyle{ AA^{-1}=I }[/math].

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**Counter-Example(s):****See:**Identity Matrix.

## References

### 2014

- http://mathworld.wolfram.com/MatrixInverse.html
- QUOTE: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix [math]\displaystyle{ A^{-1} }[/math] such that :[math]\displaystyle{ AA^{-1}=I, (1) }[/math] where I is the identity matrix. Courant and Hilbert (1989, p. 10) use the notation [math]\displaystyle{ A^_ }[/math] to denote the inverse matrix.
A square matrix A has an inverse iff the determinant |A|!=0 (Lipschutz 1991, p. 45). The so-called invertible matrix theorem is major result in linear algebra which associates the existence of a matrix inverse with a number of other equivalent properties. A matrix possessing an inverse is called nonsingular, or invertible.

The matrix inverse of a square matrix m may be taken in Mathematica using the function

`Inverse[m]`

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- QUOTE: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix [math]\displaystyle{ A^{-1} }[/math] such that :[math]\displaystyle{ AA^{-1}=I, (1) }[/math] where I is the identity matrix. Courant and Hilbert (1989, p. 10) use the notation [math]\displaystyle{ A^_ }[/math] to denote the inverse matrix.