Rotation and translation between objects with TRS matrix

I have two objects in the scene and I want that one goes in the same position of the other with the same rotation. With this I also want to store the translation and rotation that the object has done.

My idea is to create a TRS matrix that stores the translation and rotation, so that I can use it easily on the other part of the code, but when I try to move the object with this the result is wrong. Am I missing something?

 public Matrix4x4 trs;
 public void SetTRSValues(GameObject other)
     {
         Vector3 translation = other.transform.position - transform.position;
         Quaternion eulerAngles = Quaternion.FromToRotation(transform.forward, other.transform.forward);
         trs.SetTRS(translation, eulerAngles, Vector3.one);
         transform.position = trs.MultiplyPoint3x4(transform.position);
     }

If I use this method the translation and rotation work fine, but I would like to use the TRS matrix, if possible, and I would like to learn how to use the TRS matrix correctly

     public void MoveObject(GameObject other)
     {
         Vector3 translation = other.transform.position - transform.position;
         Quaternion offsetRot = Quaternion.FromToRotation(transform.forward, other.transform.forward);
         Vector3 eulerAngles = offsetRot.eulerAngles;
         transform.Rotate(eulerAngles);
         transform.position += translation;
     }

Thank you for the help