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

(A) Characteristic equation

(B) Minimal determinant

(C) Adjugate polynomial

(D) Eigenvector spectrum

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Theorem Definition:** Cayley-Hamilton theorem asserts that substituting a square matrix $A$ into its characteristic polynomial $\det(\lambda I - A) = 0$ yields the zero matrix. 2. **Stage 2: Selection:** Option A is strictly correct.

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