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BITSAT2009MathematicsDeterminantsActual

The digits ( A , B ) and ( C ) are such that the three digit numbers (A 88,6 ~B 8,86 C ) are divisible by 72 then the determinant ( | array ccc A & 6 & 8 8 & B & 6 8 & 8 & C array | ) is divisible by

Options

  1. A72
  2. B144
  3. C288
  4. D216

Correct answer

A. 72

Step-by-step solution

(R₃ 100 R₁+10 R₂+R₃ ) ( | array ccc A & 6 & 8 8 & B & 6 8 & 8 & C array |= | array ccc A & 6 & 8 8 & B & 6 A 88 & 6 B C & 86 C array | ) which is divisible by 72.

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