diff --git a/Project.toml b/Project.toml
index 5729f109..75ef585b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "FillArrays"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
-version = "0.11.4"
+version = "0.11.5"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/FillArrays.jl b/src/FillArrays.jl
index 542ac898..cbf9405a 100644
--- a/src/FillArrays.jl
+++ b/src/FillArrays.jl
@@ -380,10 +380,14 @@ const Eye{T,Axes} = RectOrDiagonal{T,Ones{T,1,Tuple{Axes}}}
 
 isone(::SquareEye) = true
 
-for f in (:permutedims, :inv, :triu, :triu!, :tril, :tril!)
-    @eval ($f)(IM::SquareEye) = IM
+# These should actually be in StdLib, LinearAlgebra.jl, for all Diagonal
+for f in (:permutedims, :triu, :triu!, :tril, :tril!)
+    @eval ($f)(IM::Diagonal{<:Any,<:AbstractFill}) = IM
 end
 
+inv(IM::SquareEye) = IM
+inv(IM::Diagonal{<:Any,<:AbstractFill}) = Diagonal(map(inv, IM.diag))
+
 Eye(n::Integer, m::Integer) = RectDiagonal(Ones(min(n,m)), n, m)
 Eye{T}(n::Integer, m::Integer) where T = RectDiagonal{T}(Ones{T}(min(n,m)), n, m)
 function Eye{T}((a,b)::NTuple{2,AbstractUnitRange{Int}}) where T
diff --git a/test/runtests.jl b/test/runtests.jl
index 7ba5c52b..37d32c82 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -926,11 +926,14 @@ end
 
 @testset "Eye identity ops" begin
     m = Eye(10)
+    D = Diagonal(Fill(2,10))
     for op in (permutedims, inv)
         @test op(m) === m
     end
+    @test permutedims(D) ≡ D
+    @test inv(D) ≡ Diagonal(Fill(1/2,10))
 
-    for m in (Eye(10), Eye(10, 10), Eye(10, 8), Eye(8, 10))
+    for m in (Eye(10), Eye(10, 10), Eye(10, 8), Eye(8, 10), D)
         for op in (tril, triu, tril!, triu!)
             @test op(m) === m
         end