Question

Assertion (A): If \(P = \begin{bmatrix}1 & 4 \\ 2 & 3 \end{bmatrix}\), then \(P^2 - 4P - 5I = 0\).
Reason (R): Every square matrix satisfies its own characteristic equation.

• A. Both (A) and (R) are correct and (R) is correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

To verify matrix equations, always use Cayley-Hamilton theorem—it simplifies calculations drastically.

Answer 1

The Correct Option is A