diff --git a/docs/src/submodules/Utilities/reference.md b/docs/src/submodules/Utilities/reference.md
index b5df0f6361..ccbeeb24ea 100644
--- a/docs/src/submodules/Utilities/reference.md
+++ b/docs/src/submodules/Utilities/reference.md
@@ -113,6 +113,7 @@ Utilities.set_index
 Utilities.set_types
 Utilities.add_set
 Utilities.rows
+Utilities.set_with_dimension
 ```
 
 ```@docs
diff --git a/src/Utilities/matrix_of_constraints.jl b/src/Utilities/matrix_of_constraints.jl
index cee2305cc1..aa0ecbfe6b 100644
--- a/src/Utilities/matrix_of_constraints.jl
+++ b/src/Utilities/matrix_of_constraints.jl
@@ -525,8 +525,53 @@ end
 
 function_constants(b::Vector, rows) = b[rows]
 
-# FIXME does not work for all sets
-set_from_constants(::Vector, ::Type{S}, rows) where {S} = S(length(rows))
+"""
+    set_with_dimension(::Type{S}, dim) where {S<:MOI.AbstractVectorSet}
+
+Returns the instance of `S` of [`MathOptInterface.dimension`](@ref) `dim`.
+This needs to be implemented for sets of type `S` to be useable with
+[`MatrixOfConstraints`](@ref).
+"""
+function set_with_dimension(::Type{S}, dim) where {S<:MOI.AbstractVectorSet}
+    return S(dim)
+end
+
+function set_with_dimension(
+    ::Type{S},
+    dim,
+) where {S<:MOI.AbstractSymmetricMatrixSetTriangle}
+    side_dimension = side_dimension_for_vectorized_dimension(dim)
+    return S(side_dimension)
+end
+
+function set_with_dimension(
+    ::Type{S},
+    dim,
+) where {S<:MOI.AbstractSymmetricMatrixSetSquare}
+    return S(isqrt(dim))
+end
+
+function set_with_dimension(::Type{MOI.LogDetConeTriangle}, dim)
+    side_dimension = side_dimension_for_vectorized_dimension(dim - 2)
+    return MOI.LogDetConeTriangle(side_dimension)
+end
+
+function set_with_dimension(::Type{MOI.LogDetConeSquare}, dim)
+    return MOI.LogDetConeSquare(isqrt(dim - 2))
+end
+
+function set_with_dimension(::Type{MOI.RootDetConeTriangle}, dim)
+    side_dimension = side_dimension_for_vectorized_dimension(dim - 1)
+    return MOI.RootDetConeTriangle(side_dimension)
+end
+
+function set_with_dimension(::Type{MOI.RootDetConeSquare}, dim)
+    return MOI.RootDetConeSquare(isqrt(dim - 1))
+end
+
+function set_from_constants(::Vector, ::Type{S}, rows) where {S}
+    return set_with_dimension(S, length(rows))
+end
 
 function MOI.get(
     model::MatrixOfConstraints,
diff --git a/test/Utilities/matrix_of_constraints.jl b/test/Utilities/matrix_of_constraints.jl
index 9b0d6bc864..d130ca662d 100644
--- a/test/Utilities/matrix_of_constraints.jl
+++ b/test/Utilities/matrix_of_constraints.jl
@@ -398,6 +398,51 @@ function test_multicone()
     return
 end
 
+MOI.Utilities.@product_of_sets(
+    MatrixSets,
+    MOI.PositiveSemidefiniteConeTriangle,
+    MOI.PositiveSemidefiniteConeSquare,
+    MOI.LogDetConeTriangle,
+    MOI.LogDetConeSquare,
+    MOI.RootDetConeTriangle,
+    MOI.RootDetConeSquare,
+)
+
+function test_matrix_sets(::Type{T} = Int) where {T}
+    model = MOI.Utilities.GenericOptimizer{
+        T,
+        MOI.Utilities.ObjectiveContainer{T},
+        MOI.Utilities.VariablesContainer{T},
+        MOI.Utilities.MatrixOfConstraints{
+            T,
+            MOI.Utilities.MutableSparseMatrixCSC{
+                T,
+                T,
+                MOI.Utilities.OneBasedIndexing,
+            },
+            Vector{T},
+            MatrixSets{T},
+        },
+    }()
+    function test_set(set)
+        MOI.empty!(model)
+        func = MOI.Utilities.zero_with_output_dimension(
+            MOI.VectorAffineFunction{T},
+            MOI.dimension(set),
+        )
+        ci = MOI.add_constraint(model, func, set)
+        MOI.Utilities.final_touch(model, nothing)
+        @test MOI.get(model, MOI.ConstraintSet(), ci) == set
+    end
+    test_set(MOI.PositiveSemidefiniteConeTriangle(2))
+    test_set(MOI.PositiveSemidefiniteConeSquare(2))
+    test_set(MOI.LogDetConeTriangle(2))
+    test_set(MOI.LogDetConeSquare(2))
+    test_set(MOI.RootDetConeTriangle(2))
+    test_set(MOI.RootDetConeSquare(2))
+    return
+end
+
 end
 
 TestMatrixOfConstraints.runtests()