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![{\displaystyle \left[\operatorname {inv} _{k}(A)\right]_{ij}={\begin{cases}{\frac {1}{a_{kk}}}&i=j=k\\-{\frac {a_{kj}}{a_{kk}}}&i=k,j\neq k\\{\frac {a_{jk}}{a_{kk}}}&i\neq k,j=k\\a_{ij}-{\frac {a_{ik}a_{kj}}{a_{kk}}}&i\neq k,j\neq k\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4b701767faabe5361f28a7e11b4c0897a21f69b6)
