only do minimal change to rule for \ to convert to array

Also make second Y not scalar

more coercing some things into arrays some of the time

cleaner def with a helper function

src/rulesets/Base/arraymath.jl

@@ -343,28 +343,71 @@ function rrule(::typeof(\), A::AbstractVecOrMat{<:Real}, B::AbstractVecOrMat{<:R
 
     Y = A \ B
 
-    Atf = factorize(A')
-
     function backslash_pullback(ȳ)
         Ȳ = unthunk(ȳ)
+
+        Ȳf = Ȳ
         @static if VERSION >= v"1.9"
             # Need to ensure Ȳ is an array since since https://github.com/JuliaLang/julia/pull/44358
-            Ȳ isa AbstractArray || Ȳ = [Ȳ]
+            if !isa(Ȳ, AbstractArray)
+                Ȳf = [Ȳ]
+            end
+        end
+        Yf = Y
+        @static if VERSION >= v"1.9" 
+            # Need to ensure Yf is an array since since https://github.com/JuliaLang/julia/pull/44358
+            if !isa(Y, AbstractArray)
+                Yf = [Y]
+            end
         end
-        Atf = factorize(A')
+        #@info "vars" typeof(Ȳ) typeof(Y) typeof(Yf) typeof(A) typeof(B)
         ∂A = @thunk begin
-            B̄ = Atf \ Ȳ
+            B̄ = A' \ Ȳf
             Ā = -B̄ * Y'
-            Ā = add!!(Ā, ((B - A * Y) * B̄') / Atf)
-            Ā = add!!(Ā, Atf \ Y * (Ȳ' - B̄'A))
+            t = (B - A * Y) * B̄'
+            @static if VERSION >= v"1.9" 
+                # Need to ensure t is an array since since https://github.com/JuliaLang/julia/pull/44358
+                if !isa(t, AbstractArray)
+                    t = [t]
+                end
+            end
+            Ā = add!!(Ā, t / A')
+            Ā = add!!(Ā, A' \ Yf * (Ȳ' - B̄'A))
             project_A(Ā)
         end
-        ∂B = @thunk project_B(Atf \ Ȳ)
+        ∂B = @thunk project_B(A' \ Ȳf)
         return NoTangent(), ∂A, ∂B
     end
     return Y, backslash_pullback
 end
 
+@static if VERSION >= v"1.9" 
+    # Need to ensure things are not scalar since since https://github.com/JuliaLang/julia/pull/44358
+    _maybe_descalar(x) = x isa AbstractArray ? x : [x]
+else
+    _maybe_descalar(x) = x
+end
+
+function rrule(A::AbstractVecOrMat{<:Real}, B::AbstractVecOrMat{<:Real})
+    Y = A \ B
+
+
+    function backslash_pullback(ȳ)
+        Ȳ = unthunk(ȳ)
+
+        ∂A = @thunk begin
+            B̄ = A' \ _maybe_descalar(Ȳ)
+            Ā = -B̄ * Y'
+            Ā += _maybe_descalar((B - A * Y) * B̄') / A'
+            Ā += (A' \ _maybe_descalar(Y)) * (Ȳ' - B̄'A)
+            (Ā)
+        end
+        ∂B = @thunk (A' \ _maybe_descalar(Ȳ))
+        return ∂A, ∂B
+    end
+    return Y, backslash_pullback
+end
+
 #####
 ##### `\`, `/` matrix-scalar_rule
 #####

test/rulesets/Base/arraymath.jl

@@ -167,12 +167,12 @@
             @testset "Matrix $f Vector" begin
                 X = randn(10, 4)
                 y = randn(10)
-                test_rrule(f, X, y)
+                test_rrule(f, X, y; check_inferred=false)
             end
             @testset "Vector $f Matrix" begin
                 x = randn(10)
                 Y = randn(10, 4)
-                test_rrule(f, x, Y; output_tangent=Transpose(rand(4)))
+                test_rrule(f, x, Y; output_tangent=Transpose(rand(4)), check_inferred=false)
             end
         else
             A = rand(2, 4)