GATE 2010 MA Eigen Values

Question

Answer 1

1. Each eigenvalue of the real skew-symmetric matrix $A$ is either $0$ or a purely imaginary number.
2. The rank of $A$ is even.

The given is matrix is of $3 \times 3$, from this we can say that rank of this matrix can only be $2$ which is only even number $> 1$

So to make rank $2$ there exist an eigen value $0$