Let $$A=\begin{pmatrix}
1 & 1 & 5\\
0 & 2 & 0\\
0 & 0 & 2
\end{pmatrix},\qquad B=\begin{pmatrix}
1 & 7 & 0\\
0 & 2 & 7\\
0 & 0 & 2
\end{pmatrix}.$$
How to prove that these two matrices are similar?
Well, I tried to prove that above characteristic polynomial of both matrices …, but it isn't correct. Because they have same elements on main diagonal,I thought that is easier to calculate, but it's not enough condition to prove that.
Can you give me some idea? Thank you
Best Answer
$A - 2I$ and $B - 2I$ (where $I$ denotes the identity matrix) do not have the same rank. So, the matrices can't be similar.