The correct option is C (a-b) (b-c) (c-a)
∣∣
∣
∣∣1aa21bb21cc2∣∣
∣
∣∣=∣∣
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∣∣0a−ba2−b20b−cb2−c21cc2∣∣
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∣∣,byR1→R1−R2R2→R2−R3
=(a−b)(b−c)∣∣
∣∣01a+b01b+c1cc2∣∣
∣∣=(a−b)(b−c)∣∣
∣∣00a−c01b+c1cc2∣∣
∣∣,byR1→R1−R2=(a−b)(b−c)(a−c)∣∣
∣∣00101b+c1cc2∣∣
∣∣
= (a-b) (b-c) (a-c). (-1) = (a-b) (b-c) (c-a).