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After investigating #54090, I found that the issue was not caused by the effects of `checksquare`, but by the use of the `@simd` macro within `tr(::Matrix)`: https://github.com/JuliaLang/julia/blob/0945b9d7740855c82a09fed42fbf6bc561e02c77/stdlib/LinearAlgebra/src/dense.jl#L373-L380 While simply removing the `@simd` macro was considered, the strict left-to-right summation without `@simd` otherwise is not necessarily more accurate, so I concluded that the problem lies in the test code, which tests the (strict) equality of two different `tr` execution results. I have modified the test code to use `≈` instead of `==`. - fixes #54090
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