Chapter 4.1, Problem 16E

Using Eq.(4), apply the singularity test to the matrices in Exercises 13-16. Show that there is no real scalar $\lambda$ such that $A-\lambda I$ is singular. [Note: Complex eigenvalues are discussed in Section 4.6.]

$A=\left[\begin{array}{cc}1& -1\\ 1& 1\end{array}\right]$