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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