diff --git a/stdlib/LinearAlgebra/src/matmul.jl b/stdlib/LinearAlgebra/src/matmul.jl
index ad8d8e91af299..c065c692a06ef 100644
--- a/stdlib/LinearAlgebra/src/matmul.jl
+++ b/stdlib/LinearAlgebra/src/matmul.jl
@@ -930,164 +930,143 @@ end
 
 
 # multiply 2x2 matrices
-function matmul2x2(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S}) where {T,S}
+Base.@constprop :aggressive function matmul2x2(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S}) where {T,S}
     matmul2x2!(similar(B, promote_op(matprod, T, S), 2, 2), tA, tB, A, B)
 end
 
-function matmul2x2!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix,
-                    _add::MulAddMul = MulAddMul())
+function __matmul_checks(C, A, B, sz)
     require_one_based_indexing(C, A, B)
     if C === A || B === C
         throw(ArgumentError("output matrix must not be aliased with input matrix"))
     end
-    if !(size(A) == size(B) == size(C) == (2,2))
+    if !(size(A) == size(B) == size(C) == sz)
         throw(DimensionMismatch(lazy"A has size $(size(A)), B has size $(size(B)), C has size $(size(C))"))
     end
+    return nothing
+end
+
+# separate function with the core of matmul2x2! that doesn't depend on a MulAddMul
+Base.@constprop :aggressive function _matmul2x2_elements(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix)
+    __matmul_checks(C, A, B, (2,2))
+    __matmul2x2_elements(tA, tB, A, B)
+end
+Base.@constprop :aggressive function __matmul2x2_elements(tA, A::AbstractMatrix)
     @inbounds begin
-    if tA == 'N'
+    tA_uc = uppercase(tA) # possibly unwrap a WrapperChar
+    if tA_uc == 'N'
         A11 = A[1,1]; A12 = A[1,2]; A21 = A[2,1]; A22 = A[2,2]
-    elseif tA == 'T'
+    elseif tA_uc == 'T'
         # TODO making these lazy could improve perf
         A11 = copy(transpose(A[1,1])); A12 = copy(transpose(A[2,1]))
         A21 = copy(transpose(A[1,2])); A22 = copy(transpose(A[2,2]))
-    elseif tA == 'C'
+    elseif tA_uc == 'C'
         # TODO making these lazy could improve perf
         A11 = copy(A[1,1]'); A12 = copy(A[2,1]')
         A21 = copy(A[1,2]'); A22 = copy(A[2,2]')
-    elseif tA == 'S'
-        A11 = symmetric(A[1,1], :U); A12 = A[1,2]
-        A21 = copy(transpose(A[1,2])); A22 = symmetric(A[2,2], :U)
-    elseif tA == 's'
-        A11 = symmetric(A[1,1], :L); A12 = copy(transpose(A[2,1]))
-        A21 = A[2,1]; A22 = symmetric(A[2,2], :L)
-    elseif tA == 'H'
-        A11 = hermitian(A[1,1], :U); A12 = A[1,2]
-        A21 = copy(adjoint(A[1,2])); A22 = hermitian(A[2,2], :U)
-    else # if tA == 'h'
-        A11 = hermitian(A[1,1], :L); A12 = copy(adjoint(A[2,1]))
-        A21 = A[2,1]; A22 = hermitian(A[2,2], :L)
-    end
-    if tB == 'N'
-        B11 = B[1,1]; B12 = B[1,2];
-        B21 = B[2,1]; B22 = B[2,2]
-    elseif tB == 'T'
-        # TODO making these lazy could improve perf
-        B11 = copy(transpose(B[1,1])); B12 = copy(transpose(B[2,1]))
-        B21 = copy(transpose(B[1,2])); B22 = copy(transpose(B[2,2]))
-    elseif tB == 'C'
-        # TODO making these lazy could improve perf
-        B11 = copy(B[1,1]'); B12 = copy(B[2,1]')
-        B21 = copy(B[1,2]'); B22 = copy(B[2,2]')
-    elseif tB == 'S'
-        B11 = symmetric(B[1,1], :U); B12 = B[1,2]
-        B21 = copy(transpose(B[1,2])); B22 = symmetric(B[2,2], :U)
-    elseif tB == 's'
-        B11 = symmetric(B[1,1], :L); B12 = copy(transpose(B[2,1]))
-        B21 = B[2,1]; B22 = symmetric(B[2,2], :L)
-    elseif tB == 'H'
-        B11 = hermitian(B[1,1], :U); B12 = B[1,2]
-        B21 = copy(adjoint(B[1,2])); B22 = hermitian(B[2,2], :U)
-    else # if tB == 'h'
-        B11 = hermitian(B[1,1], :L); B12 = copy(adjoint(B[2,1]))
-        B21 = B[2,1]; B22 = hermitian(B[2,2], :L)
+    elseif tA_uc == 'S'
+        if isuppercase(tA) # tA == 'S'
+            A11 = symmetric(A[1,1], :U); A12 = A[1,2]
+            A21 = copy(transpose(A[1,2])); A22 = symmetric(A[2,2], :U)
+        else
+            A11 = symmetric(A[1,1], :L); A12 = copy(transpose(A[2,1]))
+            A21 = A[2,1]; A22 = symmetric(A[2,2], :L)
+        end
+    elseif tA_uc == 'H'
+        if isuppercase(tA) # tA == 'H'
+            A11 = hermitian(A[1,1], :U); A12 = A[1,2]
+            A21 = copy(adjoint(A[1,2])); A22 = hermitian(A[2,2], :U)
+        else # if tA == 'h'
+            A11 = hermitian(A[1,1], :L); A12 = copy(adjoint(A[2,1]))
+            A21 = A[2,1]; A22 = hermitian(A[2,2], :L)
+        end
     end
+    end # inbounds
+    A11, A12, A21, A22
+end
+Base.@constprop :aggressive __matmul2x2_elements(tA, tB, A, B) = __matmul2x2_elements(tA, A), __matmul2x2_elements(tB, B)
+
+Base.@constprop :aggressive function matmul2x2!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix,
+                    _add::MulAddMul = MulAddMul())
+    (A11, A12, A21, A22), (B11, B12, B21, B22) = _matmul2x2_elements(C, tA, tB, A, B)
+    @inbounds begin
     _modify!(_add, A11*B11 + A12*B21, C, (1,1))
-    _modify!(_add, A11*B12 + A12*B22, C, (1,2))
     _modify!(_add, A21*B11 + A22*B21, C, (2,1))
+    _modify!(_add, A11*B12 + A12*B22, C, (1,2))
     _modify!(_add, A21*B12 + A22*B22, C, (2,2))
     end # inbounds
     C
 end
 
 # Multiply 3x3 matrices
-function matmul3x3(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S}) where {T,S}
+Base.@constprop :aggressive function matmul3x3(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S}) where {T,S}
     matmul3x3!(similar(B, promote_op(matprod, T, S), 3, 3), tA, tB, A, B)
 end
 
-function matmul3x3!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix,
-                    _add::MulAddMul = MulAddMul())
-    require_one_based_indexing(C, A, B)
-    if C === A || B === C
-        throw(ArgumentError("output matrix must not be aliased with input matrix"))
-    end
-    if !(size(A) == size(B) == size(C) == (3,3))
-        throw(DimensionMismatch(lazy"A has size $(size(A)), B has size $(size(B)), C has size $(size(C))"))
-    end
+# separate function with the core of matmul3x3! that doesn't depend on a MulAddMul
+Base.@constprop :aggressive function _matmul3x3_elements(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix)
+    __matmul_checks(C, A, B, (3,3))
+    __matmul3x3_elements(tA, tB, A, B)
+end
+Base.@constprop :aggressive function __matmul3x3_elements(tA, A::AbstractMatrix)
     @inbounds begin
-    if tA == 'N'
+    tA_uc = uppercase(tA) # possibly unwrap a WrapperChar
+    if tA_uc == 'N'
         A11 = A[1,1]; A12 = A[1,2]; A13 = A[1,3]
         A21 = A[2,1]; A22 = A[2,2]; A23 = A[2,3]
         A31 = A[3,1]; A32 = A[3,2]; A33 = A[3,3]
-    elseif tA == 'T'
+    elseif tA_uc == 'T'
         # TODO making these lazy could improve perf
         A11 = copy(transpose(A[1,1])); A12 = copy(transpose(A[2,1])); A13 = copy(transpose(A[3,1]))
         A21 = copy(transpose(A[1,2])); A22 = copy(transpose(A[2,2])); A23 = copy(transpose(A[3,2]))
         A31 = copy(transpose(A[1,3])); A32 = copy(transpose(A[2,3])); A33 = copy(transpose(A[3,3]))
-    elseif tA == 'C'
+    elseif tA_uc == 'C'
         # TODO making these lazy could improve perf
         A11 = copy(A[1,1]'); A12 = copy(A[2,1]'); A13 = copy(A[3,1]')
         A21 = copy(A[1,2]'); A22 = copy(A[2,2]'); A23 = copy(A[3,2]')
         A31 = copy(A[1,3]'); A32 = copy(A[2,3]'); A33 = copy(A[3,3]')
-    elseif tA == 'S'
-        A11 = symmetric(A[1,1], :U); A12 = A[1,2]; A13 = A[1,3]
-        A21 = copy(transpose(A[1,2])); A22 = symmetric(A[2,2], :U); A23 = A[2,3]
-        A31 = copy(transpose(A[1,3])); A32 = copy(transpose(A[2,3])); A33 = symmetric(A[3,3], :U)
-    elseif tA == 's'
-        A11 = symmetric(A[1,1], :L); A12 = copy(transpose(A[2,1])); A13 = copy(transpose(A[3,1]))
-        A21 = A[2,1]; A22 = symmetric(A[2,2], :L); A23 = copy(transpose(A[3,2]))
-        A31 = A[3,1]; A32 = A[3,2]; A33 = symmetric(A[3,3], :L)
-    elseif tA == 'H'
-        A11 = hermitian(A[1,1], :U); A12 = A[1,2]; A13 = A[1,3]
-        A21 = copy(adjoint(A[1,2])); A22 = hermitian(A[2,2], :U); A23 = A[2,3]
-        A31 = copy(adjoint(A[1,3])); A32 = copy(adjoint(A[2,3])); A33 = hermitian(A[3,3], :U)
-    else # if tA == 'h'
-        A11 = hermitian(A[1,1], :L); A12 = copy(adjoint(A[2,1])); A13 = copy(adjoint(A[3,1]))
-        A21 = A[2,1]; A22 = hermitian(A[2,2], :L); A23 = copy(adjoint(A[3,2]))
-        A31 = A[3,1]; A32 = A[3,2]; A33 = hermitian(A[3,3], :L)
+    elseif tA_uc == 'S'
+        if isuppercase(tA) # tA == 'S'
+            A11 = symmetric(A[1,1], :U); A12 = A[1,2]; A13 = A[1,3]
+            A21 = copy(transpose(A[1,2])); A22 = symmetric(A[2,2], :U); A23 = A[2,3]
+            A31 = copy(transpose(A[1,3])); A32 = copy(transpose(A[2,3])); A33 = symmetric(A[3,3], :U)
+        else
+            A11 = symmetric(A[1,1], :L); A12 = copy(transpose(A[2,1])); A13 = copy(transpose(A[3,1]))
+            A21 = A[2,1]; A22 = symmetric(A[2,2], :L); A23 = copy(transpose(A[3,2]))
+            A31 = A[3,1]; A32 = A[3,2]; A33 = symmetric(A[3,3], :L)
+        end
+    elseif tA_uc == 'H'
+        if isuppercase(tA) # tA == 'H'
+            A11 = hermitian(A[1,1], :U); A12 = A[1,2]; A13 = A[1,3]
+            A21 = copy(adjoint(A[1,2])); A22 = hermitian(A[2,2], :U); A23 = A[2,3]
+            A31 = copy(adjoint(A[1,3])); A32 = copy(adjoint(A[2,3])); A33 = hermitian(A[3,3], :U)
+        else # if tA == 'h'
+            A11 = hermitian(A[1,1], :L); A12 = copy(adjoint(A[2,1])); A13 = copy(adjoint(A[3,1]))
+            A21 = A[2,1]; A22 = hermitian(A[2,2], :L); A23 = copy(adjoint(A[3,2]))
+            A31 = A[3,1]; A32 = A[3,2]; A33 = hermitian(A[3,3], :L)
+        end
     end
+    end # inbounds
+    A11, A12, A13, A21, A22, A23, A31, A32, A33
+end
+Base.@constprop :aggressive __matmul3x3_elements(tA, tB, A, B) = __matmul3x3_elements(tA, A), __matmul3x3_elements(tB, B)
 
-    if tB == 'N'
-        B11 = B[1,1]; B12 = B[1,2]; B13 = B[1,3]
-        B21 = B[2,1]; B22 = B[2,2]; B23 = B[2,3]
-        B31 = B[3,1]; B32 = B[3,2]; B33 = B[3,3]
-    elseif tB == 'T'
-        # TODO making these lazy could improve perf
-        B11 = copy(transpose(B[1,1])); B12 = copy(transpose(B[2,1])); B13 = copy(transpose(B[3,1]))
-        B21 = copy(transpose(B[1,2])); B22 = copy(transpose(B[2,2])); B23 = copy(transpose(B[3,2]))
-        B31 = copy(transpose(B[1,3])); B32 = copy(transpose(B[2,3])); B33 = copy(transpose(B[3,3]))
-    elseif tB == 'C'
-        # TODO making these lazy could improve perf
-        B11 = copy(B[1,1]'); B12 = copy(B[2,1]'); B13 = copy(B[3,1]')
-        B21 = copy(B[1,2]'); B22 = copy(B[2,2]'); B23 = copy(B[3,2]')
-        B31 = copy(B[1,3]'); B32 = copy(B[2,3]'); B33 = copy(B[3,3]')
-    elseif tB == 'S'
-        B11 = symmetric(B[1,1], :U); B12 = B[1,2]; B13 = B[1,3]
-        B21 = copy(transpose(B[1,2])); B22 = symmetric(B[2,2], :U); B23 = B[2,3]
-        B31 = copy(transpose(B[1,3])); B32 = copy(transpose(B[2,3])); B33 = symmetric(B[3,3], :U)
-    elseif tB == 's'
-        B11 = symmetric(B[1,1], :L); B12 = copy(transpose(B[2,1])); B13 = copy(transpose(B[3,1]))
-        B21 = B[2,1]; B22 = symmetric(B[2,2], :L); B23 = copy(transpose(B[3,2]))
-        B31 = B[3,1]; B32 = B[3,2]; B33 = symmetric(B[3,3], :L)
-    elseif tB == 'H'
-        B11 = hermitian(B[1,1], :U); B12 = B[1,2]; B13 = B[1,3]
-        B21 = copy(adjoint(B[1,2])); B22 = hermitian(B[2,2], :U); B23 = B[2,3]
-        B31 = copy(adjoint(B[1,3])); B32 = copy(adjoint(B[2,3])); B33 = hermitian(B[3,3], :U)
-    else # if tB == 'h'
-        B11 = hermitian(B[1,1], :L); B12 = copy(adjoint(B[2,1])); B13 = copy(adjoint(B[3,1]))
-        B21 = B[2,1]; B22 = hermitian(B[2,2], :L); B23 = copy(adjoint(B[3,2]))
-        B31 = B[3,1]; B32 = B[3,2]; B33 = hermitian(B[3,3], :L)
-    end
+Base.@constprop :aggressive function matmul3x3!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix,
+                    _add::MulAddMul = MulAddMul())
 
-    _modify!(_add, A11*B11 + A12*B21 + A13*B31, C, (1,1))
-    _modify!(_add, A11*B12 + A12*B22 + A13*B32, C, (1,2))
-    _modify!(_add, A11*B13 + A12*B23 + A13*B33, C, (1,3))
+    (A11, A12, A13, A21, A22, A23, A31, A32, A33),
+        (B11, B12, B13, B21, B22, B23, B31, B32, B33) = _matmul3x3_elements(C, tA, tB, A, B)
 
+    @inbounds begin
+    _modify!(_add, A11*B11 + A12*B21 + A13*B31, C, (1,1))
     _modify!(_add, A21*B11 + A22*B21 + A23*B31, C, (2,1))
-    _modify!(_add, A21*B12 + A22*B22 + A23*B32, C, (2,2))
-    _modify!(_add, A21*B13 + A22*B23 + A23*B33, C, (2,3))
-
     _modify!(_add, A31*B11 + A32*B21 + A33*B31, C, (3,1))
+
+    _modify!(_add, A11*B12 + A12*B22 + A13*B32, C, (1,2))
+    _modify!(_add, A21*B12 + A22*B22 + A23*B32, C, (2,2))
     _modify!(_add, A31*B12 + A32*B22 + A33*B32, C, (3,2))
+
+    _modify!(_add, A11*B13 + A12*B23 + A13*B33, C, (1,3))
+    _modify!(_add, A21*B13 + A22*B23 + A23*B33, C, (2,3))
     _modify!(_add, A31*B13 + A32*B23 + A33*B33, C, (3,3))
     end # inbounds
     C