diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
index 5663f66eac8b3..e2ad7873ed834 100644
--- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl
+++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
@@ -576,6 +576,10 @@ wrapper_char(A::Hermitian) =  WrapperChar('H', A.uplo == 'U')
 wrapper_char(A::Hermitian{<:Real}) = WrapperChar('S', A.uplo == 'U')
 wrapper_char(A::Symmetric) = WrapperChar('S', A.uplo == 'U')
 
+wrapper_char_NTC(A::AbstractArray) = uppercase(wrapper_char(A)) == 'N'
+wrapper_char_NTC(A::Union{StridedArray, Adjoint, Transpose}) = true
+wrapper_char_NTC(A::Union{Symmetric, Hermitian}) = false
+
 Base.@constprop :aggressive function wrap(A::AbstractVecOrMat, tA::AbstractChar)
     # merge the result of this before return, so that we can type-assert the return such
     # that even if the tmerge is inaccurate, inference can still identify that the
diff --git a/stdlib/LinearAlgebra/src/matmul.jl b/stdlib/LinearAlgebra/src/matmul.jl
index 3e7c0a0ecc862..d745122c3700a 100644
--- a/stdlib/LinearAlgebra/src/matmul.jl
+++ b/stdlib/LinearAlgebra/src/matmul.jl
@@ -293,15 +293,24 @@ true
 @inline mul!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat, α::Number, β::Number) = _mul!(C, A, B, α, β)
 # Add a level of indirection and specialize _mul! to avoid ambiguities in mul!
 @inline _mul!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat, α::Number, β::Number) =
-    generic_matmatmul!(
+    generic_matmatmul_wrapper!(
         C,
         wrapper_char(A),
         wrapper_char(B),
         _unwrap(A),
         _unwrap(B),
-        α, β
+        α, β,
+        Val(wrapper_char_NTC(A) & wrapper_char_NTC(B))
     )
 
+# this indirection allows is to specialize on the types of the wrappers of A and B to some extent,
+# even though the wrappers are stripped off in mul!
+# By default, we ignore the wrapper info and forward the arguments to generic_matmatmul!
+Base.@constprop :aggressive function generic_matmatmul_wrapper!(C, tA, tB, A, B, α, β, @nospecialize(val))
+    generic_matmatmul!(C, tA, tB, A, B, α, β)
+end
+
+
 """
     rmul!(A, B)
 
@@ -368,9 +377,9 @@ julia> lmul!(F.Q, B)
 """
 lmul!(A, B)
 
-# THE one big BLAS dispatch
-Base.@constprop :aggressive function generic_matmatmul!(C::StridedMatrix{T}, tA, tB, A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
-                                    α::Number, β::Number) where {T<:BlasFloat}
+# THE one big BLAS dispatch. This is split into two methods to improve latency
+Base.@constprop :aggressive function generic_matmatmul_wrapper!(C::StridedMatrix{T}, tA, tB, A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
+                                    α::Number, β::Number, ::Val{true}) where {T<:BlasFloat}
     mA, nA = lapack_size(tA, A)
     mB, nB = lapack_size(tB, B)
     if any(iszero, size(A)) || any(iszero, size(B)) || iszero(α)
@@ -389,19 +398,37 @@ Base.@constprop :aggressive function generic_matmatmul!(C::StridedMatrix{T}, tA,
     # and extract the char corresponding to the wrapper type
     tA_uc, tB_uc = uppercase(tA), uppercase(tB)
     # the map in all ensures constprop by acting on tA and tB individually, instead of looping over them.
-    if all(map(in(('N', 'T', 'C')), (tA_uc, tB_uc)))
-        if tA_uc == 'T' && tB_uc == 'N' && A === B
-            return syrk_wrapper!(C, 'T', A, α, β)
-        elseif tA_uc == 'N' && tB_uc == 'T' && A === B
-            return syrk_wrapper!(C, 'N', A, α, β)
-        elseif tA_uc == 'C' && tB_uc == 'N' && A === B
-            return herk_wrapper!(C, 'C', A, α, β)
-        elseif tA_uc == 'N' && tB_uc == 'C' && A === B
-            return herk_wrapper!(C, 'N', A, α, β)
-        else
-            return gemm_wrapper!(C, tA, tB, A, B, α, β)
+    if tA_uc == 'T' && tB_uc == 'N' && A === B
+        return syrk_wrapper!(C, 'T', A, α, β)
+    elseif tA_uc == 'N' && tB_uc == 'T' && A === B
+        return syrk_wrapper!(C, 'N', A, α, β)
+    elseif tA_uc == 'C' && tB_uc == 'N' && A === B
+        return herk_wrapper!(C, 'C', A, α, β)
+    elseif tA_uc == 'N' && tB_uc == 'C' && A === B
+        return herk_wrapper!(C, 'N', A, α, β)
+    else
+        return gemm_wrapper!(C, tA, tB, A, B, α, β)
+    end
+end
+Base.@constprop :aggressive function generic_matmatmul_wrapper!(C::StridedMatrix{T}, tA, tB, A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
+                                    α::Number, β::Number, ::Val{false}) where {T<:BlasFloat}
+    mA, nA = lapack_size(tA, A)
+    mB, nB = lapack_size(tB, B)
+    if any(iszero, size(A)) || any(iszero, size(B)) || iszero(α)
+        if size(C) != (mA, nB)
+            throw(DimensionMismatch(lazy"C has dimensions $(size(C)), should have ($mA,$nB)"))
         end
+        return _rmul_or_fill!(C, β)
+    end
+    if size(C) == size(A) == size(B) == (2,2)
+        return matmul2x2!(C, tA, tB, A, B, α, β)
+    end
+    if size(C) == size(A) == size(B) == (3,3)
+        return matmul3x3!(C, tA, tB, A, B, α, β)
     end
+    # We convert the chars to uppercase to potentially unwrap a WrapperChar,
+    # and extract the char corresponding to the wrapper type
+    tA_uc, tB_uc = uppercase(tA), uppercase(tB)
     alpha, beta = promote(α, β, zero(T))
     if alpha isa Union{Bool,T} && beta isa Union{Bool,T}
         if tA_uc == 'S' && tB_uc == 'N'
@@ -421,18 +448,13 @@ Base.@constprop :aggressive generic_matmatmul!(C::StridedMatrix{T}, tA, tB, A::S
         _add::MulAddMul = MulAddMul()) where {T<:BlasFloat} =
     generic_matmatmul!(C, tA, tB, A, B, _add.alpha, _add.beta)
 
-# Complex matrix times (transposed) real matrix. Reinterpret the first matrix to real for efficiency.
-Base.@constprop :aggressive function generic_matmatmul!(C::StridedVecOrMat{Complex{T}}, tA, tB, A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},
-                    α::Number, β::Number) where {T<:BlasReal}
-    # We convert the chars to uppercase to potentially unwrap a WrapperChar,
-    # and extract the char corresponding to the wrapper type
-    tA_uc, tB_uc = uppercase(tA), uppercase(tB)
-    # the map in all ensures constprop by acting on tA and tB individually, instead of looping over them.
-    if all(map(in(('N', 'T', 'C')), (tA_uc, tB_uc)))
-        gemm_wrapper!(C, tA, tB, A, B, α, β)
-    else
-        _generic_matmatmul!(C, wrap(A, tA), wrap(B, tB), MulAddMul(α, β))
-    end
+function generic_matmatmul_wrapper!(C::StridedVecOrMat{Complex{T}}, tA, tB, A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},
+                    α::Number, β::Number, ::Val{true}) where {T<:BlasReal}
+    gemm_wrapper!(C, tA, tB, A, B, α, β)
+end
+Base.@constprop :aggressive function generic_matmatmul_wrapper!(C::StridedVecOrMat{Complex{T}}, tA, tB, A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},
+                    α::Number, β::Number, ::Val{false}) where {T<:BlasReal}
+    _generic_matmatmul!(C, wrap(A, tA), wrap(B, tB), MulAddMul(α, β))
 end
 # legacy method
 Base.@constprop :aggressive generic_matmatmul!(C::StridedVecOrMat{Complex{T}}, tA, tB, A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},