diff --git a/src/OffsetArrays.jl b/src/OffsetArrays.jl
index 9d050094..98097d83 100644
--- a/src/OffsetArrays.jl
+++ b/src/OffsetArrays.jl
@@ -1,6 +1,7 @@
 module OffsetArrays
 
 using Base: Indices, tail, @propagate_inbounds
+
 @static if !isdefined(Base, :IdentityUnitRange)
     const IdentityUnitRange = Base.Slice
 else
@@ -45,10 +46,12 @@ OffsetArray(A::AbstractArray{T,N}, offsets::Vararg{Int,N}) where {T,N} =
     OffsetArray(A, offsets)
 OffsetArray(A::AbstractArray{T,0}) where {T} = OffsetArray(A, ())
 
+# Create an uninitialized OffsetArray with given element type
 const ArrayInitializer = Union{UndefInitializer, Missing, Nothing}
 OffsetArray{T,N}(init::ArrayInitializer, inds::Indices{N}) where {T,N} =
     OffsetArray(Array{T,N}(init, map(indexlength, inds)), map(indexoffset, inds))
 OffsetArray{T}(init::ArrayInitializer, inds::Indices{N}) where {T,N} = OffsetArray{T,N}(init, inds)
+# Same thing, but taking multiple args for offsets/indices
 OffsetArray{T,N}(init::ArrayInitializer, inds::Vararg{AbstractUnitRange,N}) where {T,N} = OffsetArray{T,N}(init, inds)
 OffsetArray{T}(init::ArrayInitializer, inds::Vararg{AbstractUnitRange,N}) where {T,N} = OffsetArray{T,N}(init, inds)
 
@@ -402,6 +405,23 @@ end
 
 no_offset_view(A::OffsetArray) = no_offset_view(parent(A))
 
+# Quick hack for matrix multiplication.
+# Ideally, one would instead improve LinearAlgebra's support of custom indexing.
+function Base.:(*)(A::OffsetMatrix, B::OffsetMatrix)
+    matmult_check_axes(A, B)
+    C = parent(A) * parent(B)
+    OffsetArray{eltype(C), 2, typeof(C)}(C, (A.offsets[1], B.offsets[2]))
+end
+
+function Base.:(*)(A::OffsetMatrix, B::OffsetVector)
+    matmult_check_axes(A, B)
+    C = parent(A) * parent(B)
+    OffsetArray{eltype(C), 1, typeof(C)}(C, (A.offsets[1], ))
+end
+function matmult_check_axes(A, B)
+    axes(A, 2) === axes(B, 1) || axes(A, 2) == axes(B, 1) || 
+        error("axes(A,2) = $(UnitRange(axes(A,2))) does not equal axes(B,1) = $(UnitRange(axes(B,1)))")
+end
 
 ####
 # work around for segfault in searchsorted*
diff --git a/test/runtests.jl b/test/runtests.jl
index 1721621f..b2aca0b5 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -946,3 +946,34 @@ end
     @test searchsorted(o,  5) ==  2:2
     @test searchsorted(o,  6) ==  3:2
 end
+
+@testset "Matrix multiplication" begin
+    a = [1 2; 3 4]
+    v = [5, 6]
+    oa = OffsetArray(a, (2, 2))
+    ov = OffsetVector(v, (2,))
+
+    @test parent(oa * oa) == a * a
+    @test axes(oa * oa) == axes(oa)
+
+    @test parent(oa * ov) == a * v
+    @test axes(oa * ov) == (axes(oa, 1),)
+
+    @test parent(ones(2, 2:3) * ones(2:3, 3:5)) == ones(2, 2) * ones(2, 3)
+    @test axes(ones(2, 2:3) * ones(2:3, 3:5)) == (1:2, 3:5)
+
+    @test parent(ones(2, 2:3) * ones(2:3)) == ones(2, 2) * ones(2)
+    @test axes(ones(2, 2:3) * ones(2:3)) == (1:2,)
+
+    # One-based arrays
+    oa2 = OffsetArray(a, axes(a))
+    @test oa2 * a == a * a
+    @test a * oa2 == a * a
+
+    @test oa2 * v == a * v
+    @test v' * oa2 == v' * a
+
+    @test_throws Exception zeros(2, 2:3) * zeros(2:4, 2)
+    @test_throws Exception zeros(2, 2:3) * zeros(3:4, 2)
+    @test_throws Exception zeros(2, 2:3) * zeros(2:4)
+end
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