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:

\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}

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

\begin{bmatrix}1&0&0&x\\0&1&0&y\\0&0&1&z\end{bmatrix}

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.

AA^{-1}=I

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

\begin{bmatrix}1&0&0&5\\0&1&0&-2\\0&0&1&3\end{bmatrix}

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.