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COMEDK2019MathematicsDeterminants

If A= | array lll a₁ & b₁ & c₁ a₂ & b₂ & c₂ a₃ & b₃ & c₃ array | and B= | array ccc c₁ & c₂ & c₃ a₁ & a₂ & a₃ b₁ & b₂ & b₃ array | then

Options

  1. AA=-B
  2. BA=B
  3. CB=0
  4. DB=A²

Correct answer

B. A=B

Step-by-step solution

We have, aligned A &= | array lll a₁ & b₁ & c₁ a₂ & b₂ & c₂ a₃ & b₃ & c₃ array | &= | array lll a₁ & a₂ & a₃ b₁ & b₂ & b₃ c₁ & c₂ & c₃ array | &=(-) | array lll b₁ & b₂ & b₃ a₁ & a₂ & a₃ c₁ & c₂ & c₃ array | & [ |A|= |A^ T | ] &=(-)(-) | array lll c₁ & c₂ & c₃ a₁ & a₂ & a₃ b₁ & b₂ & b₃ array |= | array lll c₁ & c₂ & c₃ a₁ & a₂ & a₃ b₁ & b₂ & b₂ array |=B [R₁ R₃ ] aligned

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