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 \reftext{def:product-real-matrices-2026a}{the matrix product definition} and $I_n$ is the identity matrix from \ref{def:identity-matrix-2026a}.

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