Question

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

Answer 1

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