I have a question where I must prove that none of the following matrices are conjugate: 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 I started by working out the characteristic polynomials since if these were different, the matrices couldn't be conjugate. But all three have the same characteristic polynomial [(1-t)^3], so that didn't help me. I'm not sure what else I can do from here. I know that if A and B are conjugate, A = QBP where Q is the inverse of the matrix P. Also, matrices are conjugate if they represent the same linear transformation after a change of basis. But I'm not sure how to apply these definitions to a specific example. Thanks in advance for any help.