`fmpz_mat_inv`

Synopsis#include <flint/fmpz_mat.h>

int fmpz_mat_inv(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A)source

Sets ( $B$ , den) to the inverse of the square matrix $A$ , so that $AB = BA = \mathit{den} \cdot I$ , and returns 1 if $A$ is nonsingular; returns 0 if $A$ is singular. $B$ may be $A$ .

Dimensions up to 2 use explicit formulas with $\mathit{den} = \det(A)$ ; larger matrices are solved against the identity matrix with fmpz_mat_solve, so that den is $\det(A)$ for dimensions up to 15 and the minimal positive denominator (the largest invariant factor of $A$ ) above.

Guides#

Exact linear algebra over the integers

Cite this page

The FLINT team, “fmpz_mat_inv (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_inv.html (generated 2026-11-02).

@misc{flint-doc-fmpz-mat-fmpz-mat-inv,
  author       = {{The FLINT team}},
  title        = {{fmpz\_mat\_inv (fmpz\_mat.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fmpz_mat/fmpz_mat_inv.html},
  note         = {Generated 2026-11-02}
}

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