diff --git a/Project.toml b/Project.toml
index 490aaad5..4655ac0b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,6 +4,7 @@ version = "1.10.8"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
 [compat]
 Adapt = "2, 3"
@@ -24,9 +25,8 @@ DistributedArrays = "aaf54ef3-cdf8-58ed-94cc-d582ad619b94"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 EllipsisNotation = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "CatIndices", "DistributedArrays", "DelimitedFiles", "Documenter", "Test", "LinearAlgebra", "EllipsisNotation", "StaticArrays", "FillArrays"]
+test = ["Aqua", "CatIndices", "DistributedArrays", "DelimitedFiles", "Documenter", "Test", "EllipsisNotation", "StaticArrays", "FillArrays"]
diff --git a/src/OffsetArrays.jl b/src/OffsetArrays.jl
index a00aedff..b46d4149 100644
--- a/src/OffsetArrays.jl
+++ b/src/OffsetArrays.jl
@@ -651,6 +651,7 @@ if isdefined(Base, :IdentityUnitRange)
     no_offset_view(a::Base.Slice) = Base.Slice(UnitRange(a))
     no_offset_view(S::SubArray) = view(parent(S), map(no_offset_view, parentindices(S))...)
 end
+no_offset_view(A::PermutedDimsArray{T,N,perm,iperm,P}) where {T,N,perm,iperm,P} = PermutedDimsArray(no_offset_view(parent(A)), perm)
 no_offset_view(a::Array) = a
 no_offset_view(i::Number) = i
 no_offset_view(A::AbstractArray) = _no_offset_view(axes(A), A)
@@ -853,6 +854,8 @@ end
 import Adapt
 Adapt.adapt_structure(to, O::OffsetArray) = parent_call(x -> Adapt.adapt(to, x), O)
 
+include("linearalgebra.jl")
+
 if Base.VERSION >= v"1.4.2"
     include("precompile.jl")
     _precompile_()
diff --git a/src/linearalgebra.jl b/src/linearalgebra.jl
new file mode 100644
index 00000000..2815ca41
--- /dev/null
+++ b/src/linearalgebra.jl
@@ -0,0 +1,56 @@
+using LinearAlgebra
+using LinearAlgebra: MulAddMul, mul!, AdjOrTrans
+
+@inline LinearAlgebra.generic_matvecmul!(C::OffsetVector, fA::Function, A::AbstractVecOrMat, B::AbstractVector,
+                            alpha, beta) = unwrap_matvecmul!(C, fA, A, B, alpha, beta)
+
+@inline function unwrap_matvecmul!(C::OffsetVector, fA, A::AbstractVecOrMat, B::AbstractVector,
+                            alpha, beta)
+
+    mB_axis = Base.axes1(B)
+    mA_axis, nA_axis = axes(fA(A))
+
+    if mB_axis != nA_axis
+        throw(DimensionMismatch("mul! can't contract axis $(UnitRange(nA_axis)) from A with axes(B) == ($(UnitRange(mB_axis)),)"))
+    end
+    if mA_axis != Base.axes1(C)
+        throw(DimensionMismatch("mul! got axes(C) == ($(UnitRange(Base.axes1(C))),), expected $(UnitRange(mA_axis))"))
+    end
+
+    mul!(no_offset_view(C), fA(no_offset_view(A)), no_offset_view(B), alpha, beta)
+    C
+end
+
+# The signatures of these differs from LinearAlgebra's *only* on C:
+@inline LinearAlgebra.generic_matmatmul!(C::OffsetMatrix, fA::Function, fB::Function, A::AbstractMatrix, B::AbstractMatrix,
+                             alpha, beta) = unwrap_matmatmul!(C, fA, fB, A, B, alpha, beta)
+
+@inline LinearAlgebra.generic_matmatmul!(C::Union{OffsetMatrix, OffsetVector}, fA::Function, fB::Function, A::AbstractVecOrMat, B::AbstractVecOrMat,
+                             alpha, beta) = unwrap_matmatmul!(C, fA, fB, A, B, alpha, beta)
+
+@inline LinearAlgebra.generic_matmatmul!(C::AdjOrTrans{<:Any, <:OffsetArray}, fA::Function, fB::Function, A::AbstractMatrix, B::AbstractMatrix,
+                             alpha, beta) = unwrap_matmatmul!(C, fA, fB, A, B, alpha, beta)
+
+@inline function unwrap_matmatmul!(C::AbstractVecOrMat, fA, fB, A::AbstractVecOrMat, B::AbstractVecOrMat,
+                             alpha, beta)
+
+    mA_axis, nA_axis = axes(fA(A))
+    mB_axis, nB_axis = axes(fB(B))
+
+    if nA_axis != mB_axis
+        throw(DimensionMismatch("mul! can't contract axis $(UnitRange(nA_axis)) from A with $(UnitRange(mB_axis)) from B"))
+    elseif mA_axis != axes(C,1)
+        throw(DimensionMismatch("mul! got axes(C,1) == $(UnitRange(axes(C,1))), expected $(UnitRange(mA_axis)) from A"))
+    elseif nB_axis != axes(C,2)
+        throw(DimensionMismatch("mul! got axes(C,2) == $(UnitRange(axes(C,2))), expected $(UnitRange(nB_axis)) from B"))
+    end
+
+    # Must be sure `no_offset_view(C)` won't match signature above! 
+    mul!(no_offset_view(C), fA(no_offset_view(A)), fB(no_offset_view(B)), alpha, beta)
+    C
+end
+
+no_offset_view(A::Adjoint) = adjoint(no_offset_view(parent(A)))
+no_offset_view(A::Transpose) = transpose(no_offset_view(parent(A)))
+no_offset_view(D::Diagonal) = Diagonal(no_offset_view(parent(D)))
+