Let $n$ be a \reftext{def:natural-numbers-2026a}{natural number} with $n\ge 2$, and let $A$ be an \reftext{def:inverse-matrix-invertible-real-square-matrix-2026a}{invertible} $n\times n$ real matrix with \reftext{def:determinant-real-square-matrix-2026a}{determinant} $\det A\ne 0$. Then

where $\operatorname{adj}(A)$ is the \reftext{def:minor-cofactor-adjugate-real-square-matrix-2026b}{adjugate} of $A$. Equivalently, for all $i,j\in\{1,\dots,n\}$,

where $C_{ji}(A)$ is the $(j,i)$ \reftext{def:minor-cofactor-adjugate-real-square-matrix-2026b}{cofactor} of $A$.

In particular, each entry of $A^{-1}$ is a polynomial in the entries of $A$ divided by $\det A$.