diff --git a/stdlib/LinearAlgebra/src/uniformscaling.jl b/stdlib/LinearAlgebra/src/uniformscaling.jl
index c59871e0641ef..13acea982e7e0 100644
--- a/stdlib/LinearAlgebra/src/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/src/uniformscaling.jl
@@ -215,8 +215,8 @@ end
 function (+)(A::AbstractMatrix, J::UniformScaling)
     checksquare(A)
     B = copy_oftype(A, Base._return_type(+, Tuple{eltype(A), typeof(J)}))
-    @inbounds for i in axes(A, 1)
-        B[i,i] += J
+    for i in intersect(axes(A,1), axes(A,2))
+        @inbounds B[i,i] += J
     end
     return B
 end
@@ -224,8 +224,8 @@ end
 function (-)(J::UniformScaling, A::AbstractMatrix)
     checksquare(A)
     B = convert(AbstractMatrix{Base._return_type(+, Tuple{eltype(A), typeof(J)})}, -A)
-    @inbounds for i in axes(A, 1)
-        B[i,i] += J
+    for i in intersect(axes(A,1), axes(A,2))
+        @inbounds B[i,i] += J
     end
     return B
 end
diff --git a/stdlib/LinearAlgebra/test/uniformscaling.jl b/stdlib/LinearAlgebra/test/uniformscaling.jl
index 27f6641657e81..0f86f0555cba7 100644
--- a/stdlib/LinearAlgebra/test/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/test/uniformscaling.jl
@@ -7,6 +7,8 @@ using Test, LinearAlgebra, Random, SparseArrays
 const BASE_TEST_PATH = joinpath(Sys.BINDIR, "..", "share", "julia", "test")
 isdefined(Main, :Quaternions) || @eval Main include(joinpath($(BASE_TEST_PATH), "testhelpers", "Quaternions.jl"))
 using .Main.Quaternions
+isdefined(Main, :OffsetArrays) || @eval Main include(joinpath($(BASE_TEST_PATH), "testhelpers", "OffsetArrays.jl"))
+using .Main.OffsetArrays
 
 Random.seed!(123)
 
@@ -504,4 +506,12 @@ end
     end
 end
 
+@testset "offset arrays" begin
+    A = OffsetArray(zeros(4,4), -1:2, 0:3)
+    @test sum(I + A) ≈ 3.0
+    @test sum(A + I) ≈ 3.0
+    @test sum(I - A) ≈ 3.0
+    @test sum(A - I) ≈ -3.0
+end
+
 end # module TestUniformscaling