Find matrix $B$ of a given equation

Question

What is the value of matrix $B$ (if all other matrices are known, square and full rank matrices), given

$$ X = A(B+C) $$

Answer 1

Just solving the equation you get $B=A^{-1} X - C$

Answer 2

Starting with $$X=A(B+C)$$ pre-multiply both sides by $A^{-1}$ to get $$A^{-1}X=B+C$$ then subtract $C$ to get $$A^{-1}X-C=B$$

Answer 3

If all matrices are $n \times n$, let us consider the case $n=1$. Which means you have real numbers $x,a,b,c$ such that

$$x=a(b+c)$$

you would extract progressively :

$$\frac{x}{a}=b+c$$

then ;

$$b=-c+\frac{x}{a}$$

What is the equivalent of these operations if you have real matrices $n \geq 2$ ?