If a, b, c are positive integers less than 13 such that
2ab + bc + ca = 0 (mod 13)
ab + 2bc + ca = 10abc (mod 13)
ab + bc + 2ca = 7abc (mod 13)
then determine the remainder when a + b + c is divided by 13.
Similar problem here: https://web2.0calc.com/questions/modular-number-theory_1#r1
Try to solve this problem using the method explained in that thread.