Inverse matrix/Field/Definition

Inverse matrix

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

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

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

$M^{-1}.$