Matrix equation solver (Mathematica) [closed]

Question

I have matrix

$$A = \left( \begin{array}{ccc} -1 & 1 & 1 \\ 2 & 3 & -1 \\ -2 & 3 & 3 \end{array} \right)$$

and matrix

$$B = \left( \begin{array}{ccc} -1 & 2 & -1 \\ 1 & 2 & -2 \\ 2 & 1 & -1 \end{array} \right)$$

And I want find a matrix $X$, for which the equation

$$ XA-B=2X$$ holds, but I don't know how to do it.

I tried

Solve[XmatA - matB - 2 X = 0],

but it gives:

Set::write: "Tag Plus in -2\ X+XmatA+{{1,-2,1},{-1,-2,2},{-2,-1,1}} is Protected."

Solve::naqs: 0 is not a quantified system of equations and inequalities.

Answer 1

It says right there - 0 is not a system of equations. It's looking at 0 as the real number, not as the zero matrix. So you need to find a way to reference the matrix $$M = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}$$ and see if there are any other problems.

However, to solve this by hand, you write the equation as $$XA - 2X = B$$ and since $$2X = 2IX = X(2I)$$you get that $$X(A-2I) = B$$ and if you (can) find $(A-2I)^{-1}$ (i.e. if it exists Spoiler alert: it does), then you may multiply by this inverse to get $$X = B(A-2I)^{-1}$$