diff --git a/src/FillArrays.jl b/src/FillArrays.jl
index 9b9f40f1..36ab4185 100644
--- a/src/FillArrays.jl
+++ b/src/FillArrays.jl
@@ -6,7 +6,7 @@ import Base: size, getindex, setindex!, IndexStyle, checkbounds, convert,
     +, -, *, /, \, diff, sum, cumsum, maximum, minimum, sort, sort!,
     any, all, axes, isone, iterate, unique, allunique, permutedims, inv,
     copy, vec, setindex!, count, ==, reshape, _throw_dmrs, map, zero,
-    show, view, in, mapreduce
+    show, view, in, mapreduce, one
 
 import LinearAlgebra: rank, svdvals!, tril, triu, tril!, triu!, diag, transpose, adjoint, fill!,
     dot, norm2, norm1, normInf, normMinusInf, normp, lmul!, rmul!, diagzero, AbstractTriangular, AdjointAbsVec, TransposeAbsVec,
@@ -336,7 +336,7 @@ axes(rd::Diagonal{<:Any,<:AbstractFill}) = (axes(rd.diag,1),axes(rd.diag,1))
 axes(T::AbstractTriangular{<:Any,<:AbstractFill}) = axes(parent(T))
 
 axes(rd::RectDiagonal) = rd.axes
-size(rd::RectDiagonal) = length.(rd.axes)
+size(rd::RectDiagonal) = map(length, rd.axes)
 
 @inline function getindex(rd::RectDiagonal{T}, i::Integer, j::Integer) where T
     @boundscheck checkbounds(rd, i, j)
@@ -551,6 +551,17 @@ zero(r::Zeros{T,N}) where {T,N} = r
 zero(r::Ones{T,N}) where {T,N} = Zeros{T,N}(r.axes)
 zero(r::Fill{T,N}) where {T,N} = Zeros{T,N}(r.axes)
 
+#########
+# oneunit
+#########
+
+function one(A::AbstractFill{T,2}) where {T}
+    Base.require_one_based_indexing(A)
+    m, n = size(A)
+    m == n || throw(ArgumentError("multiplicative identity defined only for square matrices"))
+    SquareEye{T}(m)
+end
+
 #########
 # any/all/isone/iszero
 #########
diff --git a/test/runtests.jl b/test/runtests.jl
index de8a0a7b..d66c90ff 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -398,6 +398,15 @@ end
     @test convert(Diagonal{Int}, Eye(5)) == Diagonal(ones(Int,5))
 end
 
+@testset "one" begin
+    @testset for A in Any[Eye(4), Zeros(4,4), Ones(4,4), Fill(3,4,4)]
+        B = one(A)
+        @test B * A == A * B == A
+    end
+    @test_throws ArgumentError one(Ones(3,4))
+    @test_throws ArgumentError one(Ones((3:5,4:5)))
+end
+
 @testset "Sparse vectors and matrices" begin
     @test SparseVector(Zeros(5)) ==
             SparseVector{Float64}(Zeros(5)) ==