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KCET2008MathematicsDeterminants

If A= | array ccc 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

Let [A]= [ array lll a₁ & b₁ & c₁ a₂ & b₂ & c₂ a₃ & b₃ & c₃ array ] and aligned [B] &= [ array lll c₁ & c₂ & c₃ a₁ & a₂ & a₃ b₁ & b₂ & b₃ array ]= [ array lll a₁ & a₂ & a₃ b₁ & b₂ & b₃ c₁ & c₂ & c₃ array ] &=[A]^ t aligned As we know, det ()= det () A = B

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