# Hints for solving this matrix equation

$$A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 2 & 1 \\ 0 & 1 & 1 \\ \end{bmatrix} \\$$

Solve the matrix equation: $$XA=A+2X$$ 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: $$X=(A+2X)A^{-1}$$ I would like some tips on how to solve this, thanks.

• $2X = X\times 2\times I$, which you can use to factor out the $X$ – DanielV Feb 17 '15 at 19:20

$$XA=A+2X \implies X(A-2I) =A \implies X = A(A-2I)^{-1}.$$