# Which are matrices 2×2 that commute with the matrix

Which are matrices $2\times 2$ that commute with the matrix $$\left[\begin{array}{cc}1&1\\1&1\end{array}\right]?$$

• If you multiply that matrix by a generic $2 \times 2$, you get four simultaneous equations. Have you tried solving them? – Simon S Nov 11 '14 at 10:23

Work explicitly to get $$\begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}1&1\\1&1\end{pmatrix} = \begin{pmatrix}a+b&a+b\\c+d&c+d\end{pmatrix},$$ and $$\begin{pmatrix}1&1\\1&1\end{pmatrix}\begin{pmatrix}a&b\\c&d\end{pmatrix} = \begin{pmatrix}a+c&b+d\\a+c&b+d\end{pmatrix}.$$