Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[MatrixInverse], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The function inverse computes the matrix inverse of A. An error occurs if the matrix is singular.

This function uses Cramer's rule for matrices of dimension less than or equal to 4 by 4, and for matrices with the 'sparse' indexing function.

For other matrices, the inverse is computed by applying the operations for the Gauss-Jordan reduction of A to an identity matrix of the same shape.

The command with(linalg,inverse) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

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

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

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

$\left[\begin{array}{cc}-\frac{3}{2x-3}& \frac{x}{2x-3}\\ \frac{2}{2x-3}& -\frac{1}{2x-3}\end{array}\right]$