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| − | <math>A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right)</math> | + | <math>A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right)</math> |
| + | <math>A<sup>-1</sup>\left(\begin{array}{cccc}-2&3\\3&-4\end{array}\right)</math> | ||
<h3> Theorem 1 </h3> | <h3> Theorem 1 </h3> | ||
Revision as of 06:52, 10 December 2012
Inverse of a Matrix
An n x n matrix A is said to have an inverse provided there exists an n x n matrix B such that AB = BA = In. We call B the inverse of A and denote it as A-1. Thus, AA-1 = A-1A = In. In this case, A is also called nonsingular.
Example.
$ A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right) $
$ A<sup>-1</sup>\left(\begin{array}{cccc}-2&3\\3&-4\end{array}\right) $
Theorem 1
The inverse of a matrix, if it exists, is unique
Theorem 2
If A and B are both nonsingular n x n matrices (i.e. invertible), then AB is nonsingular and (AB)-1 = B-1A-1.
