Question Bank • QB_EM_084 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Cayley–Hamilton theorem

Question Statement:

According to the Cayley-Hamilton theorem, every square matrix satisfies its own:

Options:

  • (A) Adjugate matrix equation
  • (B) Characteristic polynomial equation
  • (C) Row-reduced echelon form
  • (D) Singular value decomposition

Answer Key:

B

Step-by-Step Solution & Explanation

The Cayley-Hamilton theorem states that every square matrix $A \in \mathbb{R}^{n \times n}$ satisfies its own characteristic equation $P(\lambda) = \det(A - \lambda I) = 0$, that is, $P(A) = O$.
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