Editing Invertible matrix (section)

==== Inversion of 2 × 2 matrices ====
The ''cofactor equation'' listed above yields the following result for {{nowrap|2 × 2}} matrices. Inversion of these matrices can be done as follows:<ref>{{cite book
|title=Introduction to linear algebra
|edition=3rd
|first1=Gilbert
|last1=Strang
|publisher=SIAM
|year=2003
|isbn=978-0-9614088-9-3
|page=71
|url=https://books.google.com/books?id=Gv4pCVyoUVYC
}}, [https://books.google.com/books?id=Gv4pCVyoUVYC&pg=PA71 Chapter 2, page 71]
</ref>
: <math>\mathbf{A}^{-1} = \begin{bmatrix}
    a & b \\ c & d \\
  \end{bmatrix}^{-1} =
  \frac{1}{\det \mathbf{A}} \begin{bmatrix}
    \,\,\,d & \!\!-b \\ -c & \,a \\ 
  \end{bmatrix} =
  \frac{1}{ad - bc} \begin{bmatrix}
    \,\,\,d & \!\!-b \\ -c & \,a \\ 
  \end{bmatrix}.
</math>

This is possible because {{math|1/(''ad'' − ''bc'')}} is the [[reciprocal (mathematics)|reciprocal]] of the determinant of the matrix in question, and the same strategy could be used for other matrix sizes.

The Cayley–Hamilton method gives
: <math>\mathbf{A}^{-1} = \frac{1}{\det \mathbf{A}} \left[ \left( \operatorname{tr}\mathbf{A} \right) \mathbf{I} - \mathbf{A} \right] .</math>