MatrixInverse(A) computes the matrix inverse of the Matrix A over the field F.

The (indexed) parameter F, which specifies the domain of computation, a field, must be a Maple table/module which has the following values/exports:

F[`0`]: a constant for the zero of the ring F

F[`1`]: a constant for the (multiplicative) identity of F

F[`+`]: a procedure for adding elements of F (nary)

F[`-`]: a procedure for negating and subtracting elements of F (unary and binary)

F[`*`]: a procedure for multiplying two elements of F (commutative)

F[`/`]: a procedure for dividing two elements of F

F[`=`]: a boolean procedure for testing if two elements in F are equal

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

$Q\left[\mathrm{`0`}\right],Q\left[\mathrm{`1`}\right],Q\left[\mathrm{`+`}\right],Q\left[\mathrm{`-`}\right],Q\left[\mathrm{`*`}\right],Q\left[\mathrm{`/`}\right],Q\left[\mathrm{`=`}\right]≔0,1,\mathrm{`+`},\mathrm{`-`},\mathrm{`*`},\mathrm{`/`},\mathrm{`=`}$

$Q_0,Q_1,Q_{\mathrm{`+`}},Q_{\mathrm{`-`}},Q_{\mathrm{`*`}},Q_{\mathrm{`/`}},Q_{\mathrm{`=`}}≔0,1,\mathrm{`+`},\mathrm{`-`},\mathrm{`*`},\mathrm{`/`},\mathrm{`=`}$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,3\right]\,\left[2\,1\,2\right]\,\left[3\,2\,1\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 1& 2\\ 3& 2& 1\end{array}\right]$

$\mathrm{MatrixInverse}\left[Q\right]\left(A\right)$

$\left[\begin{array}{ccc}-\frac{3}{8}& \frac{1}{2}& \frac{1}{8}\\ \frac{1}{2}& \mathrm{-1}& \frac{1}{2}\\ \frac{1}{8}& \frac{1}{2}& -\frac{3}{8}\end{array}\right]$