How to use Identity Matrix to rearrange an equation

Question

I am trying to rearrange the following equation. I do not know where to bring the identity matrix 'I' into the equation. The last line is the answer I should have, but the line above it is the answer I got from working out.

Am I right in thinking that 'I' somehow gets brought in at line 3, where I factor out X(s)?

Thanks

Answer 1

"Number minus matrix" makes no sense. You had $sX-AX$. To factor the $X$ to the right, you need to have a product of matrices in the first term. So $$ sX-AX=sIX-AX=(sI-A)X. $$