Invertible matrix/Field/Definition

Invertible matrix

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

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

holds.