Solve this following

Question:

The matrix $A=\left(\begin{array}{cc}a b & b^{2} \\ -a^{2} & -a b\end{array}\right)$ is

A. idempotent

B. Orthogonal

C. Nilpotent

D. None of these

Solution:

Matrix $A$ is said to be nilpotent since there exist a positive integer $k=1$ such that $A k$ is zero matrix.