Let $m,n\in$ \reftext{def:natural-numbers-2026a}{$\mathbb{N}$} and let $A$ be a real $m\times n$ matrix. Let $I_m$ and $I_n$ denote the \reftext{def:identity-matrix-2026a}{identity matrices} of sizes $m$ and $n$, and let the products be taken in the sense of \ref{def:product-real-matrices-2026a}. Then

In particular, for a square matrix $A$ of size $n$, $A\,I_n=I_n\,A=A$.