If a=bc, b=ca, c=ab find abc

Fill in (2) in (1):

a=cca = > c^2=1 = > c=+1 or c=-1

Fill in (3) in (2)

b=aba = > a^2=1 = > a=+1 or a=-1

same for (1) in (2) : b=+1 or b=-1

To satisfy all conditions at the same time, a, b and c all have to be + 1 OR any two of them must be negative (e. g., a=b=-1, c=+1).

In all cases, abc=1