no it is not true. it can be shown by ur own calculation .
at last step u calculated final matrix as
1 1 3
0 -1 -4
0 0 b-8
now if we solve it , then we can c that (b-8)Z=0
therefore z= 0/(b-8)
if u put b=8 , then z=0/0 which is undefined hence except b=8 , we will get z=0 for all values of b.