Question

The eigen values of the matrix $\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$ are

• A. i and -i
• B. 1 and -1
• C. 0 and 1
• D. 0 and -1

Answer 1

The correct option is A i and -i

Charactristic equation is

$|A-\lambda I|$ = 0

or $\left|\begin{array}{cc}-\lambda & 1\\ -1& -\lambda \end{array}\right|$ = 0

$\Rightarrow$ ${\lambda }^2$ + 1 = 0

$\Rightarrow$ ${\lambda }^2$ = -1

$\Rightarrow$ $\lambda$ = i, -i