For this question, I am stuck with solving the system of equations in the field. Do I just convert the system into a matrix and then reduce to row echelon form? I am not asking for the answer, I am just asking if I have the right idea
Show that $Z_7$ is a field and solve the following system of equations in $Z_7$: $2x + 3y + 2z =1, 3x + 2y + 2z =3, x + 6y + 6z =0$.