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All the four of the 2 x 2 matrix p = are non zero, and one of its eigen values is zero. Which of the following statements is true?

P₁₁P₂₂ - P₁₂P₂₁ = 1

P₁₁P₂₂ - P₁₂P₂₁ = - 1

P₁₁P₂₂ - P₁₂P₂₁ = 0

P₁₁P₂₂ + P₁₂P₂₁ = 1

Answer : Option C

Explanation :

Use [λI - P] = 0

⇒(λ - P₁₁)(λ - P₂₂) - P₂₁P₁₂ = 0

Putting λ = 0, we get P₁₁P₂₂ - P₂₁P₁₂ = 0.

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