How to solve a system of matrix equations?

Given are two lists of 87 3x1 vectors each. I also know that when multiplying a 3x3 matrix by the nth vector of the first list, I get the nth vector of the second list. The 3x3 matrix is ​​the same in all these calculations. So it's a system of equations with 87 equations and I want to solve for the content of the 3x3 matrix. I've tried to approximate the solution with Machine Learning and Curve Fitting, but there are too few equations for that. How could I solve this problem mathematically or approximate the solution with Matlab?

[Torsten]

In a previous request, you wanted the 3x3 matrix to be a rotation matrix. Is this no longer important ?

[Torsten]

And the rotation axis in your case passes through the origin ?

Answer 1

[Matt J]

For example, given

   A=rand(3,87);
   X=rand(3,3);
   B=X*A;

you can reconstruct X by doing,

   X=B/A;

[Matt J]

In a previous request, you wanted the 3x3 matrix to be a rotation matrix. Is this no longer important ?

If the result needs to be a rotation matrix, as Torsten speculates, then you can do that with this File Exchange submission,

result=absor(A,B,'doTrans',0)

[Christoph Müßig]

Thank you very much, this perfectly solves my question :)

[Matt J]

You're welcome, but please Accept-click the answer, if that's the case.