I considered solving of the system of linear equations a¹₁ₛ₀x¹a¹₁ₛ₁+...+a¹ₙₛ₀xⁿa¹ₙₛ₁=b¹ $$...$$ aⁿ₁ₛ₀x¹aⁿ₁ₛ₁+...+aⁿₙₛ₀xⁿaⁿₙₛ₁=bⁿ over non-commutative associative algebra. I considered examples in quaternion algebra. I considered also Newton's method to solve the equation $$f(x)=a$$ over non-commutative associative algebra.
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Aleks Kleyn (2024) studied this question.
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