Is it possible to subtract a matrix from both side? I have this equation $AX + B = I$ and I want to find Matrix $X$.
$$(A^{-1})AX + B = (A^{-1})I$$
$$X + B = (A^{-1})I$$
My question is, is it legal to do $X + B - B = (A^{-1})I - B$?

$AX+B=I$, $A^{-1}AX+A^{-1}B=A^{-1}I$. So: 
$X=A^{-1}I-A^{-1}B$. It's legal.
