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.
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