Matrix/Adjugate matrix/Formula with determinant/Fact

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}M}$ denote an ${\displaystyle {}n\times n}$-matrix over ${\displaystyle {}K}$.

If ${\displaystyle {}M}$ is invertible, then

${\displaystyle {}M^{-1}={\frac {1}{\det M}}\cdot M^{\operatorname {adj} }\,.}$