###### Definition 3.1.1

An \(n\times n\) matrix \(A\) is called *invertible* if there is a matrix \(B\) such that \(BA = I_n\text{,}\) where \(I_n\) is the \(n\times n\) identity matrix. The matrix \(B\) is called the *inverse* of \(A\) and denoted \(A^{-1}\text{.}\)