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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