diff --git a/ext/LinearSolveEnzymeExt.jl b/ext/LinearSolveEnzymeExt.jl
index 26d530d19..304e302d2 100644
--- a/ext/LinearSolveEnzymeExt.jl
+++ b/ext/LinearSolveEnzymeExt.jl
@@ -9,6 +9,53 @@ using Enzyme
 
 using EnzymeCore
 
+function EnzymeCore.EnzymeRules.forward(func::Const{typeof(LinearSolve.init)}, ::Type{RT}, prob::EnzymeCore.Annotation{LP}, alg::Const; kwargs...) where {RT, LP <: LinearSolve.LinearProblem}
+    @assert !(prob isa Const)
+    res = func.val(prob.val, alg.val; kwargs...)
+    if RT <: Const
+        return res
+    end
+    dres = func.val(prob.dval, alg.val; kwargs...)
+    dres.b .= res.b == dres.b ? zero(dres.b) : dres.b
+    dres.A .= res.A == dres.A ? zero(dres.A) : dres.A
+    if RT <: DuplicatedNoNeed
+        return dres
+    elseif RT <: Duplicated
+        return Duplicated(res, dres)
+    end
+    error("Unsupported return type $RT")
+end
+
+function EnzymeCore.EnzymeRules.forward(func::Const{typeof(LinearSolve.solve!)}, ::Type{RT}, linsolve::EnzymeCore.Annotation{LP}; kwargs...) where {RT, LP <: LinearSolve.LinearCache}
+    @assert !(linsolve isa Const)
+
+    res = func.val(linsolve.val; kwargs...)
+    
+    if RT <: Const
+        return res
+    end
+    if linsolve.val.alg isa LinearSolve.AbstractKrylovSubspaceMethod
+        error("Algorithm $(_linsolve.alg) is currently not supported by Enzyme rules on LinearSolve.jl. Please open an issue on LinearSolve.jl detailing which algorithm is missing the adjoint handling")
+    end
+    b = deepcopy(linsolve.val.b)
+
+    db = linsolve.dval.b
+    dA = linsolve.dval.A
+
+    linsolve.val.b = db - dA * res.u
+    dres = func.val(linsolve.val; kwargs...)
+
+    linsolve.val.b = b
+
+    if RT <: DuplicatedNoNeed
+        return dres
+    elseif RT <: Duplicated
+        return Duplicated(res, dres)
+    end
+
+    return Duplicated(res, dres)
+end
+
 function EnzymeCore.EnzymeRules.augmented_primal(config, func::Const{typeof(LinearSolve.init)}, ::Type{RT}, prob::EnzymeCore.Annotation{LP}, alg::Const; kwargs...) where {RT, LP <: LinearSolve.LinearProblem}
     res = func.val(prob.val, alg.val; kwargs...)
     dres = if EnzymeRules.width(config) == 1
diff --git a/test/enzyme.jl b/test/enzyme.jl
index 02e071d41..89903a858 100644
--- a/test/enzyme.jl
+++ b/test/enzyme.jl
@@ -1,5 +1,7 @@
 using Enzyme, ForwardDiff
 using LinearSolve, LinearAlgebra, Test
+using FiniteDiff
+using SafeTestsets
 
 n = 4
 A = rand(n, n);
@@ -161,4 +163,54 @@ Enzyme.autodiff(Reverse, f3, Duplicated(copy(A), dA), Duplicated(copy(b1), db1),
 @test dA ≈ dA2 atol=5e-5
 @test db1 ≈ db12
 @test db2 ≈ db22
-=#
\ No newline at end of file
+=#
+
+A = rand(n, n);
+dA = zeros(n, n);
+b1 = rand(n);
+for alg in (
+    LUFactorization(), 
+    RFLUFactorization(),
+    # KrylovJL_GMRES(), fails
+    )
+    @show alg
+    function fb(b)
+        prob = LinearProblem(A, b)
+
+        sol1 = solve(prob, alg)
+
+        sum(sol1.u)
+    end
+    fb(b1)
+
+    fd_jac = FiniteDiff.finite_difference_jacobian(fb, b1) |> vec
+    @show fd_jac
+
+    en_jac = map(onehot(b1)) do db1
+        eres = Enzyme.autodiff(Forward, fb, Duplicated(copy(b1), db1))
+        eres[1]
+    end |> collect
+    @show en_jac
+
+    @test en_jac ≈ fd_jac rtol=1e-4
+
+    function fA(A)
+        prob = LinearProblem(A, b1)
+
+        sol1 = solve(prob, alg)
+
+        sum(sol1.u)
+    end
+    fA(A)
+
+    fd_jac = FiniteDiff.finite_difference_jacobian(fA, A) |> vec
+    @show fd_jac
+
+    en_jac = map(onehot(A)) do dA
+        eres = Enzyme.autodiff(Forward, fA, Duplicated(copy(A), dA))
+        eres[1]
+    end |> collect
+    @show en_jac
+
+    @test en_jac ≈ fd_jac rtol=1e-4
+end
\ No newline at end of file