Definition:Inverse Matrix

Definition
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:
 * $\mathbf A \mathbf B = \mathbf I_n = B \mathbf A$

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 $\mathbf A^{-1}$.

Also see

 * Product Inverse in Ring is Unique