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Using Cayley-Hamilton for A = [[1,2],[1,3]] whose characteristic equation is lambda<sup>2</sup> - 4lambda + 1 = 0, we get A<sup>2</sup> =

Answer: 4A - I.

A 4A - I
B 4A + I
C A + 4I
D I - 4A

Correct answer: A. 4A - I

Explanation: Cayley-Hamilton theorem: every matrix satisfies its own characteristic equation. So A² - 4A + I = 0, which rearranges to A² = 4A - I. Answer: A² = 4A - I.

Concept context

Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.

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Using Cayley-Hamilton for A = [[1,2],[1,3]] whose characteristic equation is lambda<sup>2</sup> - 4lambda + 1 = 0, we get A<sup>2</sup> =

Concept context

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