The equation is XA = A + 3X
A = \begin{pmatrix}4 & -6 & 2\\-1 & 8 & 0\\-1 & 7 & -2\end{pmatrix}
What I do:
XA - 3X = A
XA - 3X * I = A (I = the identity matrix)
X(A - 3I) = A
But I am not sure It works like that. Then I solve A - 3I by which I mean subtracting \begin{pmatrix}3 & 0 & 0\\0 & 3 & 0\\0 & 0 & 3\end{pmatrix} from A and the rest is obvious but still I don't think matrix equations work like that. I would appreciate any clues to the right directions or answer if I am doing it right.