Could you explain to me how to solve matrix equations?
Here is an example:
Prove that:
$$2X^2 + X = \begin{bmatrix} -1&5&3\\-2&1&2\\0&-4&-3\end{bmatrix}$$
has no solutions in $M(3,3;\mathbb{R})$, where $M(3,3;\mathbb{R})$ is the space of all $3\times3$ matrices with real entries.