\begin{definition}[Definition:Inverse Matrix]
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
Let $\mathbf A$ be a square matrix of order $n$.
Let there exist a square matrix $\mathbf B$ of order $n$ such that:
:$\mathbf A \mathbf B = \mathbf I_n = \mathbf B \mathbf A$
where $\mathbf I_n$ denotes the unit matrix of order $n$.
Then $\mathbf B$ is called the '''inverse of $\mathbf A$''' and is usually denoted $\mathbf A^{-1}$.
\end{definition}