A33 will only be 1 if the system of equations is consistent and has a unique solution. In this system, the 0 in A33 tells you that the system has infinitely many solutions.
5 -4 1 0
1 1 0 0
-10 8 -2 0
Switch rows 1 and 2 to make A11=1; replace row 3 with row 3 plus -2 times row 1:
1 1 0 0
5 -4 1 0
0 0 0 0
Replace row 2 with row 2 minus 5 times row 1, to make A21=0:
1 1 0 0
0 -9 1 0
0 0 0 0
The reduced system of equations is
x+y = 0
-9y+z = 0
Since both equations involve y, use y=t to define the set of solutions parametrically.
x = -y
z = 9y
y = t
x = -t
z = 9t
The system of equations has infinitely many solutions; the solution set is any triple (x,y,z) of the form (-t,t,9t).