I have a given matrix A and it is multiplied with a matrix S. The result is also given. How do I get 3x3 matrix S?
$$ A= \begin{pmatrix} 1 & 2 & 3 & 4 & 5 \\ 6 & 7 & 8 & 9 & 10\\ 0 & 0 & 1 & 0 & 0 \\ \end{pmatrix} $$ $$ SA= \begin{pmatrix} 6 & 7 & 0 & 9 & 10 \\ 1 & 2 & 0 & 4 & 5\\ 0 & 0 & 1 & 0 & 0 \\ \end{pmatrix} $$
As from the look of the matrix it has to be something obvious, but I just don't know what I should do.
What are the steps to solve this kind of problems?
The first two rows are $(0,1,-8) $ and $(1,0,-3) $. The third one you can find out.