diff --git a/Project.toml b/Project.toml
index 4fff4b82..c35adc5c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "GPUArrays"
 uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
-version = "11.5.5"
+version = "11.5.6"
 
 [workspace]
 projects = ["lib/GPUArraysCore", "lib/JLArrays", "test", "docs"]
@@ -26,7 +26,7 @@ JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
 JLD2Ext = "JLD2"
 
 [compat]
-Adapt = "4.0"
+Adapt = "4.6.1"
 GPUArraysCore = "= 0.2.0"
 JLD2 = "0.4, 0.5, 0.6"
 KernelAbstractions = "0.9.28, 0.10"
diff --git a/src/host/linalg.jl b/src/host/linalg.jl
index 999c7226..f216386f 100644
--- a/src/host/linalg.jl
+++ b/src/host/linalg.jl
@@ -530,6 +530,11 @@ end
     function LinearAlgebra.generic_matmatmul_wrapper!(C::AbstractGPUMatrix{T}, tA::AbstractChar, tB::AbstractChar, A::AbstractGPUVecOrMat{T}, B::AbstractGPUVecOrMat{T}, alpha::Number, beta::Number, val::LinearAlgebra.BlasFlag.SyrkHerkGemm) where {T}
         LinearAlgebra.generic_matmatmul!(C, tA, tB, A, B, alpha, beta)
     end
+    # Symmetric/Hermitian inputs with BLAS eltypes would otherwise dispatch to BLAS.symm!/
+    # hemm!: GPU arrays are DenseArrays, so they match the StridedMatrix{<:BlasFloat} methods
+    function LinearAlgebra.generic_matmatmul_wrapper!(C::AbstractGPUMatrix{T}, tA::AbstractChar, tB::AbstractChar, A::AbstractGPUVecOrMat{T}, B::AbstractGPUVecOrMat{T}, alpha::Number, beta::Number, val::LinearAlgebra.BlasFlag.SymmHemmGeneric) where {T}
+        LinearAlgebra.generic_matmatmul!(C, tA, tB, A, B, alpha, beta)
+    end
     # need to support mixed complex/real types too
     #function LinearAlgebra.generic_matmatmul_wrapper!(C::AbstractGPUMatrix{Complex{T}}, tA::AbstractChar, tB::AbstractChar, A::AbstractGPUVecOrMat{Complex{T}}, B::AbstractGPUVecOrMat{T}, alpha::Number, beta::Number, val::V) where {T<:BlasReal, V<:LinearAlgebra.BlasFlag.SyrkHerkGemm}
     #    LinearAlgebra.generic_matmatmul!(C, tA, tB, A, B, alpha, beta)
diff --git a/test/testsuite/linalg.jl b/test/testsuite/linalg.jl
index 1b404d96..d8e587e0 100644
--- a/test/testsuite/linalg.jl
+++ b/test/testsuite/linalg.jl
@@ -219,6 +219,45 @@
                 @test collect(Ct) ≈ C
             end
         end
+
+        @testset "mul! + Symmetric/Hermitian" begin
+            # with BLAS eltypes these dispatch through generic_matmatmul_wrapper!'s
+            # SymmHemmGeneric path, which must not end up in BLAS.symm!/hemm!
+            @testset "$W{$T}, uplo=$uplo" for T in (Float32, ComplexF32), W in (Symmetric, Hermitian), uplo in (:U, :L)
+                if !(T in eltypes)
+                    continue
+                end
+                n = 128
+                A = AT(rand(T, n, n))
+                B = AT(rand(T, n, n))
+                b = AT(rand(T, n))
+
+                # matrix-matrix, wrapped on either side
+                Ct = AT(zeros(T, n, n))
+                C = zeros(T, n, n)
+                mul!(Ct, W(A, uplo), B)
+                mul!(C, W(collect(A), uplo), collect(B))
+                @test collect(Ct) ≈ C
+
+                mul!(Ct, B, W(A, uplo))
+                mul!(C, collect(B), W(collect(A), uplo))
+                @test collect(Ct) ≈ C
+
+                # general case: α≠1 and β≠0 together
+                Et = AT(rand(T, n, n))
+                E = collect(Et)
+                mul!(Et, W(A, uplo), B, 3, 2)
+                mul!(E, W(collect(A), uplo), collect(B), 3, 2)
+                @test collect(Et) ≈ E
+
+                # matrix-vector
+                ct = AT(zeros(T, n))
+                c = zeros(T, n)
+                mul!(ct, W(A, uplo), b)
+                mul!(c, W(collect(A), uplo), collect(b))
+                @test collect(ct) ≈ c
+            end
+        end
     end
 
     @testset "diagm" begin