diff --git a/src/FESpaces/Pullbacks.jl b/src/FESpaces/Pullbacks.jl
index 0b05d2403..8afd972a6 100644
--- a/src/FESpaces/Pullbacks.jl
+++ b/src/FESpaces/Pullbacks.jl
@@ -11,7 +11,7 @@ function get_cell_dof_basis(
   )
   cell_ref_dofs = lazy_map(get_dof_basis, cell_reffe)
   cell_phy_dofs = lazy_map(inverse_map(Pullback(pushforward)), cell_ref_dofs, cell_args...)
-  return lazy_map(linear_combination, cell_change, cell_phy_dofs) # TODO: Inverse
+  return lazy_map(linear_combination, cell_change, cell_phy_dofs) # TODO: Inverse and transpose
 end
 
 function get_cell_shapefuns(
diff --git a/src/ReferenceFEs/Pullbacks.jl b/src/ReferenceFEs/Pullbacks.jl
index 46602b495..bbdf1ddda 100644
--- a/src/ReferenceFEs/Pullbacks.jl
+++ b/src/ReferenceFEs/Pullbacks.jl
@@ -229,7 +229,6 @@ struct CoVariantPiolaMap <: Pushforward end
 function evaluate!(
   cache, ::CoVariantPiolaMap, v_ref::Number, Jt::Number
 )
-  # we right-multiply to compute the gradient correctly
   return v_ref ⋅ transpose(inv(Jt))
 end
 
diff --git a/src/ReferenceFEs/ReferenceFEInterfaces.jl b/src/ReferenceFEs/ReferenceFEInterfaces.jl
index ead616c1f..a4b1c0b82 100644
--- a/src/ReferenceFEs/ReferenceFEInterfaces.jl
+++ b/src/ReferenceFEs/ReferenceFEInterfaces.jl
@@ -390,11 +390,11 @@ associated with the dof basis `predofs` and the basis `shapefuns`.
 
 It is equivalent to
 
-    change = inv(evaluate(predofs,shapefuns))
+    change = transpose(inv(evaluate(predofs,shapefuns)))
     linear_combination(change,predofs) # i.e. transpose(change)*predofs
 """
 function compute_dofs(predofs,shapefuns)
-  change = inv(evaluate(predofs,shapefuns))
+  change = transpose(inv(evaluate(predofs,shapefuns)))
   linear_combination(change,predofs)
 end