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I use the latest NCAlgebra package (5.0) for non-commutative algebra.

<< NC` 
<< NCAlgebra`
NCSolve[a**x==b,x]

How do I solve for the variable x, assuming there is an inverse for a? Somehow this code does not output any solution. Can you help?

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I found the NCGBX methods (Gröbner Basis). This problem is easily solved in the following way:

<<NC`
<<NCAlgebra`
<<NCGBX`
SetKnowns[a,b,inv[a]]
SetUnknowns[x]
NCMakeGB[{a**x==b},10]

This returns:

{x -> a^-1 ** b}

as expected. I had to include the inverse $a^{-1}$ into the SetKnowns list. (Commutative or non-commutative) Algebras assume a ring structure among its definition properties, which does not include the existence of multiplicative inverses, in its most general case.

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