diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl
index 9cbe3f76ccfb9..77799ea888d91 100644
--- a/stdlib/LinearAlgebra/src/generic.jl
+++ b/stdlib/LinearAlgebra/src/generic.jl
@@ -1155,6 +1155,9 @@ function (/)(A::AbstractVecOrMat, B::AbstractVecOrMat)
     size(A,2) != size(B,2) && throw(DimensionMismatch("Both inputs should have the same number of columns"))
     return copy(adjoint(adjoint(B) \ adjoint(A)))
 end
+# \(A::StridedMatrix,x::Number) = inv(A)*x Should be added at some point when the old elementwise version has been deprecated long enough
+# /(x::Number,A::StridedMatrix) = x*inv(A)
+/(x::Number, v::AbstractVector) = x*pinv(v)
 
 cond(x::Number) = iszero(x) ? Inf : 1.0
 cond(x::Number, p) = cond(x)
diff --git a/stdlib/LinearAlgebra/test/dense.jl b/stdlib/LinearAlgebra/test/dense.jl
index efeedf93ebd1f..c2ab5df107527 100644
--- a/stdlib/LinearAlgebra/test/dense.jl
+++ b/stdlib/LinearAlgebra/test/dense.jl
@@ -1129,12 +1129,12 @@ end
 end
 
 function test_rdiv_pinv_consistency(a, b)
-    @test a*(b/b) ≈ (a*b)*pinv(b) ≈ a*(b*pinv(b))
-    @test typeof(a*(b/b)) == typeof((a*b)*pinv(b)) == typeof(a*(b*pinv(b)))
+    @test (a*b)/b ≈ a*(b/b) ≈ (a*b)*pinv(b) ≈ a*(b*pinv(b))
+    @test typeof((a*b)/b) == typeof(a*(b/b)) == typeof((a*b)*pinv(b)) == typeof(a*(b*pinv(b)))
 end
 function test_ldiv_pinv_consistency(a, b)
-    @test (a\a)*b ≈ (pinv(a)*a)*b ≈ pinv(a)*(a*b)
-    @test typeof((a\a)*b) == typeof((pinv(a)*a)*b) == typeof(pinv(a)*(a*b))
+    @test a\(a*b) ≈ (a\a)*b ≈ (pinv(a)*a)*b ≈ pinv(a)*(a*b)
+    @test typeof(a\(a*b)) == typeof((a\a)*b) == typeof((pinv(a)*a)*b) == typeof(pinv(a)*(a*b))
 end
 function test_div_pinv_consistency(a, b)
     test_rdiv_pinv_consistency(a, b)