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I tried to solve the system of equations $$xa=ax$$ $$yb=by$$ $$xy=u$$ where $a,b,u$ are known invertible matrices and x and y are unknown matrices. I tried Mathematica and Python but couldn't get it right. Assuming

  • $a=[[31,57,47],[95,63,23],[21,19,13]]$,
  • $b=[[21,46,17],[69,24,27],[33,18,51]]$,
  • $u=[[98,85,90],[81,73,2],[74,63,73]]$.

I tried this Mathematica code

A = {{31, 57, 2}, {95, 63, 23}, {21, 19, 13}};
B = {{21, 46, 17}, {69, 24, 27}, {33, 18, 51}};
U = {{96, 85, 90}, {81, 73, 2}, {74, 63, 73}};
X = Array[x, Dimensions[A]];
Y = Array[y, Dimensions[B]];
eqs = Thread[Flatten[{A . X - X . A, B . Y - Y . B, U - X . Y}] == 0]
Solve[Take[eqs, 27]]
Solve[eqs]
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