Inverse Matrix and Invertible Real Square Matrix

Let $n\in\mathbb{N}$, and let $A$ and $B$ be $n\times n$ real matrices. We say that $B$ is an inverse of $A$ if

where matrix multiplication is the product from the matrix product definition and $I_n$ is the identity matrix from Identity Matrix.

A real $n\times n$ matrix $A$ is called invertible if there exists an $n\times n$ real matrix $B$ that is an inverse of $A$. If $A$ is invertible, its inverse is unique, and we denote the unique inverse by