diff --git a/base/deprecated.jl b/base/deprecated.jl
index 4165ed3574a3a..88cc32b94c4d9 100644
--- a/base/deprecated.jl
+++ b/base/deprecated.jl
@@ -1058,4 +1058,22 @@ function reduced_dims0(dims::Dims, region)
     map(last, reduced_dims0(map(n->OneTo(n), dims), region))
 end
 
+# #18218
+eval(Base.LinAlg, quote
+    function arithtype(T)
+        depwarn(string("arithtype is now deprecated. If you were using it inside a ",
+            "promote_op call, use promote_op(LinAlg.matprod, Ts...) instead. Otherwise, ",
+            "if you need its functionality, consider defining it locally."),
+            :arithtype)
+        T
+    end
+    function arithtype(::Type{Bool})
+        depwarn(string("arithtype is now deprecated. If you were using it inside a ",
+            "promote_op call, use promote_op(LinAlg.matprod, Ts...) instead. Otherwise, ",
+            "if you need its functionality, consider defining it locally."),
+            :arithtype)
+        Int
+    end
+end)
+
 # End deprecations scheduled for 0.6
diff --git a/base/linalg/matmul.jl b/base/linalg/matmul.jl
index 6352912f0b9db..64c280d574b67 100644
--- a/base/linalg/matmul.jl
+++ b/base/linalg/matmul.jl
@@ -2,8 +2,7 @@
 
 # matmul.jl: Everything to do with dense matrix multiplication
 
-arithtype(T) = T
-arithtype(::Type{Bool}) = Int
+matprod(x, y) = x*y + x*y
 
 # multiply by diagonal matrix as vector
 function scale!(C::AbstractMatrix, A::AbstractMatrix, b::AbstractVector)
@@ -76,11 +75,11 @@ At_mul_B{T<:BlasComplex}(x::StridedVector{T}, y::StridedVector{T}) = [BLAS.dotu(
 
 # Matrix-vector multiplication
 function (*){T<:BlasFloat,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     A_mul_B!(similar(x, TS, size(A,1)), A, convert(AbstractVector{TS}, x))
 end
 function (*){T,S}(A::AbstractMatrix{T}, x::AbstractVector{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     A_mul_B!(similar(x,TS,size(A,1)),A,x)
 end
 (*)(A::AbstractVector, B::AbstractMatrix) = reshape(A,length(A),1)*B
@@ -99,22 +98,22 @@ end
 A_mul_B!(y::AbstractVector, A::AbstractVecOrMat, x::AbstractVector) = generic_matvecmul!(y, 'N', A, x)
 
 function At_mul_B{T<:BlasFloat,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     At_mul_B!(similar(x,TS,size(A,2)), A, convert(AbstractVector{TS}, x))
 end
 function At_mul_B{T,S}(A::AbstractMatrix{T}, x::AbstractVector{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     At_mul_B!(similar(x,TS,size(A,2)), A, x)
 end
 At_mul_B!{T<:BlasFloat}(y::StridedVector{T}, A::StridedVecOrMat{T}, x::StridedVector{T}) = gemv!(y, 'T', A, x)
 At_mul_B!(y::AbstractVector, A::AbstractVecOrMat, x::AbstractVector) = generic_matvecmul!(y, 'T', A, x)
 
 function Ac_mul_B{T<:BlasFloat,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     Ac_mul_B!(similar(x,TS,size(A,2)),A,convert(AbstractVector{TS},x))
 end
 function Ac_mul_B{T,S}(A::AbstractMatrix{T}, x::AbstractVector{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     Ac_mul_B!(similar(x,TS,size(A,2)), A, x)
 end
 
@@ -132,7 +131,7 @@ Ac_mul_B!(y::AbstractVector, A::AbstractVecOrMat, x::AbstractVector) = generic_m
 Matrix multiplication.
 """
 function (*){T,S}(A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     A_mul_B!(similar(B, TS, (size(A,1), size(B,2))), A, B)
 end
 A_mul_B!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = gemm_wrapper!(C, 'N', 'N', A, B)
@@ -166,14 +165,14 @@ julia> Y
 A_mul_B!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat) = generic_matmatmul!(C, 'N', 'N', A, B)
 
 function At_mul_B{T,S}(A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     At_mul_B!(similar(B, TS, (size(A,2), size(B,2))), A, B)
 end
 At_mul_B!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = A===B ? syrk_wrapper!(C, 'T', A) : gemm_wrapper!(C, 'T', 'N', A, B)
 At_mul_B!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat) = generic_matmatmul!(C, 'T', 'N', A, B)
 
 function A_mul_Bt{T,S}(A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     A_mul_Bt!(similar(B, TS, (size(A,1), size(B,1))), A, B)
 end
 A_mul_Bt!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = A===B ? syrk_wrapper!(C, 'N', A) : gemm_wrapper!(C, 'N', 'T', A, B)
@@ -190,7 +189,7 @@ end
 A_mul_Bt!(C::AbstractVecOrMat, A::AbstractVecOrMat, B::AbstractVecOrMat) = generic_matmatmul!(C, 'N', 'T', A, B)
 
 function At_mul_Bt{T,S}(A::AbstractMatrix{T}, B::AbstractVecOrMat{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     At_mul_Bt!(similar(B, TS, (size(A,2), size(B,1))), A, B)
 end
 At_mul_Bt!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = gemm_wrapper!(C, 'T', 'T', A, B)
@@ -199,7 +198,7 @@ At_mul_Bt!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat) = generi
 Ac_mul_B{T<:BlasReal}(A::StridedMatrix{T}, B::StridedMatrix{T}) = At_mul_B(A, B)
 Ac_mul_B!{T<:BlasReal}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = At_mul_B!(C, A, B)
 function Ac_mul_B{T,S}(A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     Ac_mul_B!(similar(B, TS, (size(A,2), size(B,2))), A, B)
 end
 Ac_mul_B!{T<:BlasComplex}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = A===B ? herk_wrapper!(C,'C',A) : gemm_wrapper!(C,'C', 'N', A, B)
@@ -208,14 +207,14 @@ Ac_mul_B!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat) = generic
 A_mul_Bc{T<:BlasFloat,S<:BlasReal}(A::StridedMatrix{T}, B::StridedMatrix{S}) = A_mul_Bt(A, B)
 A_mul_Bc!{T<:BlasFloat,S<:BlasReal}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{S}) = A_mul_Bt!(C, A, B)
 function A_mul_Bc{T,S}(A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    TS = promote_op(*, arithtype(T), arithtype(S))
+    TS = promote_op(matprod, T, S)
     A_mul_Bc!(similar(B,TS,(size(A,1),size(B,1))),A,B)
 end
 A_mul_Bc!{T<:BlasComplex}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = A===B ? herk_wrapper!(C, 'N', A) : gemm_wrapper!(C, 'N', 'C', A, B)
 A_mul_Bc!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat) = generic_matmatmul!(C, 'N', 'C', A, B)
 
 Ac_mul_Bc{T,S}(A::AbstractMatrix{T}, B::AbstractMatrix{S}) =
-    Ac_mul_Bc!(similar(B, promote_op(*, arithtype(T), arithtype(S)), (size(A,2), size(B,1))), A, B)
+    Ac_mul_Bc!(similar(B, promote_op(matprod, T, S), (size(A,2), size(B,1))), A, B)
 Ac_mul_Bc!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = gemm_wrapper!(C, 'C', 'C', A, B)
 Ac_mul_Bc!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat) = generic_matmatmul!(C, 'C', 'C', A, B)
 Ac_mul_Bt!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat) = generic_matmatmul!(C, 'C', 'T', A, B)
@@ -448,7 +447,7 @@ end
 function generic_matmatmul{T,S}(tA, tB, A::AbstractVecOrMat{T}, B::AbstractMatrix{S})
     mA, nA = lapack_size(tA, A)
     mB, nB = lapack_size(tB, B)
-    C = similar(B, promote_op(*, arithtype(T), arithtype(S)), mA, nB)
+    C = similar(B, promote_op(matprod, T, S), mA, nB)
     generic_matmatmul!(C, tA, tB, A, B)
 end
 
@@ -642,7 +641,7 @@ end
 
 # multiply 2x2 matrices
 function matmul2x2{T,S}(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    matmul2x2!(similar(B, promote_op(*, T, S), 2, 2), tA, tB, A, B)
+    matmul2x2!(similar(B, promote_op(matprod, T, S), 2, 2), tA, tB, A, B)
 end
 
 function matmul2x2!{T,S,R}(C::AbstractMatrix{R}, tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})
@@ -671,7 +670,7 @@ end
 
 # Multiply 3x3 matrices
 function matmul3x3{T,S}(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    matmul3x3!(similar(B, promote_op(*, T, S), 3, 3), tA, tB, A, B)
+    matmul3x3!(similar(B, promote_op(matprod, T, S), 3, 3), tA, tB, A, B)
 end
 
 function matmul3x3!{T,S,R}(C::AbstractMatrix{R}, tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})
diff --git a/test/linalg/matmul.jl b/test/linalg/matmul.jl
index 10b71597a4c89..b5321150fcec4 100644
--- a/test/linalg/matmul.jl
+++ b/test/linalg/matmul.jl
@@ -389,3 +389,30 @@ let
         @test_throws DimensionMismatch A_mul_B!(full43, full43, tri44)
     end
 end
+
+# #18218
+module TestPR18218
+    using Base.Test
+    import Base.*, Base.+, Base.zero
+    immutable TypeA
+        x::Int
+    end
+    Base.convert(::Type{TypeA}, x::Int) = TypeA(x)
+    immutable TypeB
+        x::Int
+    end
+    immutable TypeC
+        x::Int
+    end
+    Base.convert(::Type{TypeC}, x::Int) = TypeC(x)
+    zero(c::TypeC) = TypeC(0)
+    zero(::Type{TypeC}) = TypeC(0)
+    (*)(x::Int, a::TypeA) = TypeB(x*a.x)
+    (*)(a::TypeA, x::Int) = TypeB(a.x*x)
+    (+)(a::Union{TypeB,TypeC}, b::Union{TypeB,TypeC}) = TypeC(a.x+b.x)
+    A = TypeA[1 2; 3 4]
+    b = [1, 2]
+    d = A * b
+    @test typeof(d) == Vector{TypeC}
+    @test d == TypeC[5, 11]
+end