diff --git a/src/group_operations/multiplication_operation.jl b/src/group_operations/multiplication_operation.jl
index b9f376b..7966543 100644
--- a/src/group_operations/multiplication_operation.jl
+++ b/src/group_operations/multiplication_operation.jl
@@ -15,8 +15,12 @@ A group operation that is realised by a matrix multiplication.
 struct MatrixMultiplicationGroupOperation <: AbstractMultiplicationGroupOperation end
 
 Base.:*(e::Identity{<:AbstractMultiplicationGroupOperation}) = e
-Base.:*(::Identity{MatrixMultiplicationGroupOperation}, p::AbstractMatrix) = p
-Base.:*(p::AbstractMatrix, ::Identity{MatrixMultiplicationGroupOperation}) = p
+Base.:*(::Identity{MatrixMultiplicationGroupOperation}, p::Union{AbstractMatrix,Number}) = p
+function Base.:*(
+    p::Union{AbstractMatrix,Number}, ::Identity{MatrixMultiplicationGroupOperation}
+)
+    return p
+end
 function Base.:*(
     e::Identity{<:AbstractMultiplicationGroupOperation},
     ::Identity{<:AbstractMultiplicationGroupOperation},
diff --git a/test/operations/test_multiplication_operation.jl b/test/operations/test_multiplication_operation.jl
new file mode 100644
index 0000000..04f2fc7
--- /dev/null
+++ b/test/operations/test_multiplication_operation.jl
@@ -0,0 +1,19 @@
+using LieGroups, Test
+
+@testset "Addition Operation" begin
+    @testset "Base.:+ and Base.:- with the Identity" begin
+        e = Identity(MatrixMultiplicationGroupOperation())
+        @test (e * e) === e
+        g = 2
+        @test (g * e) == g
+        @test (e * g) == g
+        @test (g / e) == g
+        @test (e \ g) == g
+        @test (e / g) == 1 / g
+        @test (g \ e) == 1 / g
+        @test (e / e) === e
+        @test (e \ e) === e
+        @test inv(e) === e
+        @test det(e)
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 0eaeaba..bd02722 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -15,6 +15,7 @@ end
     end
     @testset "Generic Group Operations" begin
         include_test("operations/test_addidion_operation.jl")
+        include_test("operations/test_multiplication_operation.jl")
     end
     @testset "Generic Group Actions" begin
         include_test("actions/test_action_interface.jl")