solve symbolic matrix from matrix equation

I have the symbolic math toolbox within Matlab 2012a. Try to solve the problem:

R*M = M*T where R=[R1, R2, R3, R4], T=[T1, T2, T3, T4] are known 4*4 matrix. M is an unknown 4*4 matrix. How may I solve it without explicitly extract 4 equations from each of three R/T pairs? Assume 16 equations will solve 4*4=16 unknowns in M.

I know I may be able to do but would like a better way than manually set up the equations:

syms M11 M21 ... 
equation1 = R(1,1)*M11+R(1,2)*M21+R(1,3)*M31+R(1,4)*M41 == M11*T(1,1) + M12*T(2,1) + M13*T(3,1) + M14*T(4,1) 
equation2 = ..........
..........
t = solve([equation1 , equation2, ..........]);

Thanks.

[Karan Gill]

Can you post your code? Your question is hard to understand.

Answer 1

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/328335-matrix-with-entries-as-variable#answer_257492