Matrix Equation - Make X the Subject

Question

I'm having a complete mind blank here even though i'm pretty sure the solution is relatively easy.

I need to make X the subject of the following equation:

$$AB - AX = X $$

All i've done so far is: $$A(B-X) = X$$ $$B-X = A^{-1} X$$

Not sure if thats right?

Thanks in advance.

Answer 1

Whatever you have written is correct if inverse of A exists.

Hint for another way of writing an expression for $X$: $AB = (I+A)X.$

Answer 2

Continuing with your expression, $B-X = A^{-1} X$, $B = (I+A^{-1}) X$, $X = (I+A^{-1})^{-1}B$.