I have two sets of $10\times 10$ matrices M1,M2,M3,M4,M5 and N1,N2,N3,N4,N5 and I want to solve a set of equations for these matrices

Solve[{trafomatrix.M1.Inverse[trafomatrix] == N1, trafomatrix.M2.Inverse[trafomatrix] == N2, trafomatrix.M3.Inverse[trafomatrix] == N3, trafomatrix.My4.Inverse[trafomatrix] == N4, trafomatrix.M5.Inverse[trafomatrix] == N5 }, {?????}]

The thing I'm looking for is a $10\times 10$ matrix which I called above trafomatrix. Is there any way to tell Mathematica that is solve for this $10 \times 10$ matrix with arbitrary entries?

Of course a very ugly workaround would be to define, by hand, a $10\times 10 $ matrix with 100 variable names in it and then specify at the end of solve these 100 variables.

I have two sets of $10\times 10$ matrices $M1,M2,M3,M4,M5$ and $N1,N2,N3,N4,N5$ and I want to solve a set of equations for these matrices

Solve[{
  trafomatrix.M1.Inverse[trafomatrix] == N1,
  trafomatrix.M2.Inverse[trafomatrix] == N2,
  trafomatrix.M3.Inverse[trafomatrix] == N3,
  trafomatrix.M4.Inverse[trafomatrix] == N4,
  trafomatrix.M5.Inverse[trafomatrix] == N5},
  {?????}
]

The thing I'm looking for is a $10\times 10$ matrix which I called above trafomatrix. Is there any way to tell Mathematica that is solve for this $10 \times 10$ matrix with arbitrary entries?

Of course a very ugly workaround would be to define, by hand, a $10\times 10 $ matrix with 100 variable names in it and then specify these 100 variables at the end of Solve.