Inverse matrix/Field/Definition

Let ${\displaystyle {}K}$ denote a field. For an invertible matrix ${\displaystyle {}M\in \operatorname {Mat} _{n}(K)}$, the matrix ${\displaystyle {}A\in \operatorname {Mat} _{n}(K)}$ fulfilling

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

is called the inverse matrix of ${\displaystyle {}M}$. It is denoted by

${\displaystyle M^{-1}.}$