\begin{equation} A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 2 & 1 \\ 0 & 1 & 1 \\ \end{bmatrix} \\ \end{equation}
Solve the matrix equation: \begin{equation} XA=A+2X \end{equation} Where $X$ is a matrix. If I have understood the problem correctly $X$ is $3x3$.
I was thinking maybe I could use the Identity matrix and get something like: \begin{equation} X=(A+2X)A^{-1} \end{equation} I would like some tips on how to solve this, thanks.
Advance as
$$ XA=A+2X \implies X(A-2I) =A \implies X = A(A-2I)^{-1}. $$