6x-18y-30z=-24
-3x+13y+19z=16
2x-8y-17z=-25

I need the identity matrix

I think you mean you must solve this via Gaussian elimination?

An 3-by-3 identity matrix is just:



If you solve your system you will have a matrix that looks like:



where x, y, and z are your solutions to the system.

An identity matrix is what we get when we multiply an invertible matrix by its inverse.



Upon solving via rref(reduced row echelon form) your matrix will look like so:



I assume this is what you mean by an identity matrix?

Technically, that's not an identity matrix. It is reduced row echelon form.

I am not going to step through it all, but at least you know what you're shooting for.