diff --git a/gap/elements.gi b/gap/elements.gi
index d0f19c0..a8bd995 100644
--- a/gap/elements.gi
+++ b/gap/elements.gi
@@ -32,14 +32,14 @@ InstallMethod( \=, "for two elements of a quasigroup",
     IsIdenticalObj,
     [ IsQuasigroupElmRep, IsQuasigroupElmRep ],
 function( x, y )
-    return FamilyObj( x ) = FamilyObj( y ) and x![ 1 ] = y![ 1 ];
+    return x![ 1 ] = y![ 1 ];
 end );
 
 InstallMethod( \<, "for two elements of a quasigroup",
     IsIdenticalObj,
     [ IsQuasigroupElmRep, IsQuasigroupElmRep ],
 function( x, y )
-    return FamilyObj( x ) = FamilyObj( y ) and x![ 1 ] < y![ 1 ];
+    return x![ 1 ] < y![ 1 ];
 end );
 
 InstallMethod( \., "for quasigroup and positive integer",
diff --git a/gap/quasigroups.gi b/gap/quasigroups.gi
index 8a3d276..41565c2 100644
--- a/gap/quasigroups.gi
+++ b/gap/quasigroups.gi
@@ -866,9 +866,9 @@ InstallMethod( Opposite, "for magma",
     M -> ConstructorFromTable(M)( TransposedMat( MultiplicationTable( M ) ) )
 );
 
-InstallMethod( Opposite, "for magma",
-    [ IsMagma and HasCayleyTable], # mult table easy if Cayley table there
-    M -> ConstructorFromTable(M)( TransposedMat( MultiplicationTable( M ) ) )
+InstallMethod( Opposite, "for quasigroup",
+    [ IsQuasigroup ],  # Might not have a multiplication table 
+    M -> ConstructorFromTable(M)( TransposedMat( CayleyTable( M ) ) )
 );
 
 #############################################################################