Invertible matrix/Field/Definition

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}M}$ denote an ${\displaystyle {}n\times n}$-matrix over ${\displaystyle {}K}$. Then ${\displaystyle {}M}$ is called invertible if there exists a matrix ${\displaystyle {}A\in \operatorname {Mat} _{n}(K)}$ such that

${\displaystyle {}A\circ M=E_{n}=M\circ A\,}$

holds.