Hello, I need to solve the following matrice equation. The known matrices are A & B.

AX + 3IX = B

If anyone could help me here I would appreciate it.

I figured it would look something like this, though I am not sure:

$\displaystyle AX + 3IX = B$

$\displaystyle inv(A)AX + 3IX = inv(A)B$

$\displaystyle X + 3IX = inv(A)B$

$\displaystyle X + inv(3I)(3I)X = inv(3I)inv(A)B$

$\displaystyle 2X = inv(3I)inv(A)B$

IF this is correct how would I count the inverse of3I? I would be the identity matrix of course, it is all 3 in a diagonal instead of 1?

Thanks in advance.