The Adjoint(A) command constructs Matrix M such that $A·M=\mathrm{Determinant}\left(A\right)·\mathrm{IdentityMatrix}\left(\mathrm{Dimensions}\left(A\right)\right)$.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$A≔⟨⟨9\,4\,1⟩\left|⟨1\,3\,-1⟩\right|⟨0\,8\,1⟩⟩\:$

$C≔\mathrm{Adjoint}\left(A\right)$

$C≔\left[\begin{array}{ccc}11& \mathrm{-1}& 8\\ 4& 9& \mathrm{-72}\\ \mathrm{-7}& 10& 23\end{array}\right]$

$A·C$

$\left[\begin{array}{ccc}103& 0& 0\\ 0& 103& 0\\ 0& 0& 103\end{array}\right]$

$\mathrm{Determinant}\left(A\right)$

$103$