If matrix satisfies , which condition MUST hold?
Answer and explanation
Correct answer: A. Trace(M) = 0 and Det(M) = 0
- Step 1: By the Cayley-Hamilton theorem: . Step 2. If , then . Step 3. Then . For non-zero nilpotent matrices, this requires . Answer: Trace(M) = 0 and Det(M) = 0. Why not the others: Nilpotent matrices have zero trace and zero determinant.
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