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<h1> Inverse of a Matrix </h1> | <h1> Inverse of a Matrix </h1> | ||

− | <p> An <i>n</i> x <i>n</i> matrix <i>A</i> is said to have an inverse provided there exists an <i>n</i> x <i>n</i> matrix <i>B</i> such that <i>AB</i> = <i>BA</i> = <i>I</i>. We call <i>B</i> the inverse of <i>A</i> and denote it as <i>A</i><sup>-1</sup>. In this case, A is also called nonsingular. | + | <p> An <i>n</i> x <i>n</i> matrix <i>A</i> is said to have an inverse provided there exists an <i>n</i> x <i>n</i> matrix <i>B</i> such that <i>AB</i> = <i>BA</i> = <i>I</i><sub>n</sub>. We call <i>B</i> the inverse of <i>A</i> and denote it as <i>A</i><sup>-1</sup>. Thus, <i>A</i><i>A</i><sup>-1</sup> = <i>A</i><sup>-1</sup><i>A</i> = <i>I</i><sub>n</sub>. In this case, A is also called nonsingular. |

## Revision as of 06:43, 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* = *I*_{n}. We call *B* the inverse of *A* and denote it as *A*^{-1}. Thus, *A**A*^{-1} = *A*^{-1}*A* = *I*_{n}. In this case, A is also called nonsingular.