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GATE ECE 2008 | Question-1


All the four entries of the $2 \times 2$ matrix $\mathbf{P}=\left[\begin{array}{ll}p_{11} & p_{12} \\ p_{21} & p_{22}\end{array}\right]$ are nonzero, and one of its eigenvalues is zero. Which of the following statements is true?

  1. $p_{11} p_{22}-p_{12} p_{21}=1$
  2. $p_{11} p_{22}-p_{12} p_{21}=-1$
  3. $p_{11} p_{22}-p_{12} p_{21}=0$
  4. $p_{11} p_{22}+p_{12} p_{21}=0$
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