# 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.