Question

All the four entries of the 2 x 2 matric $P=\left[\begin{array}{cc}{P}_{11}& P_{12}\\ P_{21}& P_{22}\end{array}\right]$ are nonzero, and one of its eigenvalues is zero. Which of the following statements is true?

• A. $P_{11}{P}_{22}-P_{12}{P}_{21}=1$
• B. $P_{11}{P}_{22}-P_{12}{P}_{21}=-1$
• C. $P_{11}{P}_{22}-P_{12}{P}_{21}=0$
• D. $P_{11}{P}_{22}+P_{12}{P}_{21}=0$

Answer 1

The correct option is C $P_{11}{P}_{22}-P_{12}{P}_{21}=0$

$|P|=$ Product of eigen values = 0
$\Rightarrow P_{11}{P}_{22}-P_{12}{P}_{21}=0$