Answer to Question #193025 in Linear Algebra for prince

Question

Find det(C) if

C = λ λ + 1

λ λ − 1

Answer 1

If

$C = \left( {\begin{matrix} \lambda &{\lambda + 1}\\ \lambda &{\lambda - 1} \end{matrix}} \right)$

Then

$\det (C) = \lambda \left( {\lambda - 1} \right) - \lambda \left( {\lambda + 1} \right) = {\lambda ^2} - \lambda - {\lambda ^2} - \lambda = - 2\lambda$

Answer: $- 2\lambda$