diff --git a/doc/matrix.autodoc b/doc/matrix.autodoc
index d32dcae..a4b0e5c 100644
--- a/doc/matrix.autodoc
+++ b/doc/matrix.autodoc
@@ -215,7 +215,27 @@ z,z^2
 <Attr Name="Determinant" Arg="mat" Label="for a Singular matrix"/>
 <Attr Name="DeterminantMat" Arg="mat" Label="for a Singular matrix"/>
 <Description>
-TODO
+
+Return the determinant of the square matrix <A>mat</A>.
+
+<Example><![CDATA[
+gap> r := SI_ring( );
+<singular ring, 3 indeterminates>
+gap> m := SI_matrix( r, 2, 3, "x,y,z,x^2,y^2,z^2" );
+<singular matrix, 2x3>
+gap> Display( m );
+x,  y,  z,
+x^2,y^2,z^2
+gap> n := m * SI_transpose( m );
+<singular matrix, 2x2>
+gap> SI_det( n );
+x^4*y^2-2*x^3*y^3+x^2*y^4+x^4*z^2+y^4*z^2-2*x^3*z^3-2*y^3*z^3+x^2*z^4+y^2*z^4
+gap> N := SI_module( n );
+<singular module, 2 vectors in free module of rank 2>
+gap> SI_det( N );
+x^4*y^2-2*x^3*y^3+x^2*y^4+x^4*z^2+y^4*z^2-2*x^3*z^3-2*y^3*z^3+x^2*z^4+y^2*z^4
+]]></Example>
+
 </Description>
 </ManSection>