I would like to find all matrices that commute with matrix $ A =\begin{pmatrix}1 & -1 \\ 0 & 1 \end{pmatrix}$
Proposed solution
$\begin{pmatrix}a&b \\c &d\end{pmatrix}\begin{pmatrix}1&-1 \\0 &1\end{pmatrix} = \begin{pmatrix}1& -1\\ 0&1\end{pmatrix}\begin{pmatrix}a&b \\ c&d\end{pmatrix} = \begin{pmatrix}a& -a+b\\ c&-c+d\end{pmatrix}=\begin{pmatrix}a-c& b-d\\ c&d\end{pmatrix}$
Unclear about the following
$a=a-c$
$-a+b =b-d$
$c=c$
$-c+d=d$
So any matrix of the form $\begin{pmatrix}d & 0 \\ 0 & a\end{pmatrix}$
Please could someone review and correct if needs be
Thanks