Without expanding the determinant, prove that 
Multiplying row 1 with a, row 2 with b and row 3 with c
[R1→ aR1, R2→ bR2, R3→ cR3]
[Taking common abc from C3]
[Applying C1↔ C3]
= 
[Applying C2 ↔ C3]
= RHS
Since, LHS = RHS
∴ the given result is proved.
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