diff --git a/Project.toml b/Project.toml
index 4f5f210..91a8710 100644
--- a/Project.toml
+++ b/Project.toml
@@ -7,6 +7,7 @@ Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DataAPI = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
 GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
@@ -14,6 +15,7 @@ Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
 [weakdeps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
@@ -22,6 +24,7 @@ StructArraysAdaptExt = "Adapt"
 StructArraysGPUArraysCoreExt = "GPUArraysCore"
 StructArraysSparseArraysExt = "SparseArrays"
 StructArraysStaticArraysExt = "StaticArrays"
+StructArraysLinearAlgebraExt = "LinearAlgebra"
 
 [compat]
 Adapt = "3.4"
@@ -29,6 +32,7 @@ ConstructionBase = "1"
 DataAPI = "1"
 GPUArraysCore = "0.1.2"
 InfiniteArrays = "0.13"
+LinearAlgebra = "1"
 StaticArrays = "1.5.6"
 Tables = "1"
 julia = "1.6"
diff --git a/ext/StructArraysLinearAlgebraExt.jl b/ext/StructArraysLinearAlgebraExt.jl
new file mode 100644
index 0000000..ebb562d
--- /dev/null
+++ b/ext/StructArraysLinearAlgebraExt.jl
@@ -0,0 +1,17 @@
+module StructArraysLinearAlgebraExt
+
+using StructArrays
+using LinearAlgebra
+import LinearAlgebra: mul!
+
+const StructMatrixC{T, A<:AbstractMatrix{T}} = StructArrays.StructMatrix{Complex{T}, @NamedTuple{re::A, im::A}}
+
+function mul!(C::StructMatrixC, A::StructMatrixC, B::StructMatrixC, alpha::Number, beta::Number)
+	mul!(C.re, A.re, B.re, alpha, beta)
+	mul!(C.re, A.im, B.im, -alpha, oneunit(beta))
+	mul!(C.im, A.re, B.im, alpha, beta)
+	mul!(C.im, A.im, B.re, alpha, oneunit(beta))
+	C
+end
+
+end
diff --git a/src/StructArrays.jl b/src/StructArrays.jl
index 7c1b1dd..57058ce 100644
--- a/src/StructArrays.jl
+++ b/src/StructArrays.jl
@@ -30,6 +30,7 @@ end
     include("../ext/StructArraysGPUArraysCoreExt.jl")
     include("../ext/StructArraysSparseArraysExt.jl")
     include("../ext/StructArraysStaticArraysExt.jl")
+    include("../ext/StructArraysLinearAlgebraExt.jl")
 end
 
 end # module
diff --git a/src/structarray.jl b/src/structarray.jl
index 64ff17a..239c5d7 100644
--- a/src/structarray.jl
+++ b/src/structarray.jl
@@ -106,6 +106,7 @@ _structarray(args::Tuple, ::Tuple) = _structarray(args, nothing)
 _structarray(args::NTuple{N, Any}, names::NTuple{N, Symbol}) where {N} = StructArray(NamedTuple{names}(args))
 
 const StructVector{T, C<:Tup, I} = StructArray{T, 1, C, I}
+const StructMatrix{T, C<:Tup, I} = StructArray{T, 2, C, I}
 StructVector{T}(args...; kwargs...) where {T} = StructArray{T}(args...; kwargs...)
 StructVector(args...; kwargs...) = StructArray(args...; kwargs...)
 
diff --git a/test/runtests.jl b/test/runtests.jl
index ed6f573..9e97115 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1510,3 +1510,13 @@ end
     S = StructArray{Complex{Int}}((1:∞, 1:∞))
     @test Base.IteratorSize(S) == Base.IsInfinite()
 end
+
+@testset "LinearAlgebra" begin
+    @testset "matrix * matrix" begin
+        A = StructArray{ComplexF64}((rand(10,10), rand(10,10)))
+        B = StructArray{ComplexF64}((rand(10,10), rand(10,10)))
+        MA, MB = Matrix(A), Matrix(B)
+        @test A * B ≈ MA * MB
+        @test A * A ≈ MA * MA
+    end
+end