Using properties of determinants prove that:
Operating R1→aR1, R2→bR2, R3→cR3
Taking a, b, c common from C1, C2, C3 respectively
Operating R1→R1- R3, R2→R2- R3
Taking (a+b+c) common from R1, R2
Operating R3→ R3- R1- R2
Operating C1→aC1, C2→bC2
Operating C1→C1+C3, C2→C2+C3
Taking a, b, 2ab from R1, R2, R3
Expanding with R3
1