The Cayley–Hamilton theorem asserts that every square matrix satisfies its own:
Options:
(A) Characteristic equation
(B) Minimal polynomial only if symmetric
(C) Diagonal Jordan form
(D) Determinantal inverse
Answer Key:
A
Step-by-Step Solution & Explanation
The Cayley–Hamilton theorem states that if $p(\lambda) = \det(A - \lambda I) = 0$ is the characteristic equation of an $n \times n$ matrix $A$, then substituting matrix $A$ into $p$ yields $p(A) = 0$, the zero matrix. Thus, every square matrix satisfies its own characteristic equation.