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Wrong eltype in 3-arg * #1291

@mcabbott

Description

@mcabbott

Here matrix-matrix-scalar multiplication seems to make incorrect assumptions about what number type scalar multiplication will return:

julia> import Unitful

julia> a = 2.0Unitful.cm
2.0 cm

julia> b = 0.1Unitful.cm
0.1 cm

julia> a * [a b; -b a] * [a b; -b a]  # avoids the fast path, as Number not assumed to commute
2×2 Matrix{Unitful.Quantity{Float64, 𝐋³, Unitful.FreeUnits{(cm³,), 𝐋³, nothing}}}:
  7.98 cm³  0.8 cm³
 -0.8 cm³   7.98 cm³

julia> [a b; -b a] * [a b; -b a] * a  # uses fast path mat_mat_scalar
ERROR: DimensionError: 8.0 cm³ and 0.0 cm are not dimensionally compatible.
Stacktrace:
  [1] _muladd
    @ ~/.julia/packages/Unitful/nwwOk/src/quantities.jl:197 [inlined]
  [2] muladd
    @ ~/.julia/packages/Unitful/nwwOk/src/quantities.jl:192 [inlined]
  [3] macro expansion
    @ ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:897 [inlined]
  [4] macro expansion
    @ ./simdloop.jl:77 [inlined]
  [5] _generic_matmatmul!(C::Matrix{…}, A::Matrix{…}, B::Matrix{…}, _add::LinearAlgebra.MulAddMul{…})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:896
  [6] generic_matmatmul!
    @ ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:868 [inlined]
  [7] _mul!
    @ ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:287 [inlined]
  [8] mul!
    @ ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:285 [inlined]
  [9] _mat_mat_scalar
    @ ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:1167 [inlined]
 [10] mat_mat_scalar
    @ ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:1161 [inlined]
 [11] *(A::Matrix{Unitful.Quantity{…}}, B::Matrix{Unitful.Quantity{…}}, γ::Unitful.Quantity{Float64, 𝐋, Unitful.FreeUnits{…}})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/matmul.jl:1122
 [12] top-level scope
    @ REPL[419]:1
Some type information was truncated. Use `show(err)` to see complete types.

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