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Question 17007 – Reasoning
December 12, 2023
GATE 1994
December 13, 2023
Question 17007 – Reasoning
December 12, 2023
GATE 1994
December 13, 2023

GATE 1993

Question 14

If the matrix A4, calculated by the use of Cayley-Hamilton theorem or otherwise, is _________

A
A4 = I
Question 14 Explanation: 
Let λ be eigen value, then characteristic equation will be
(1-λ) (-1-λ) (i-λ) (-i-λ)
= (λ2-1) (λ2+1)
= λ4-1
Characteristic equation is λ4-1 = 0.
According to Cayley-Hamilton theorem, every matrix satisfies its own characteristic equation, so
A4 = I
Correct Answer: A
Question 14 Explanation: 
Let λ be eigen value, then characteristic equation will be
(1-λ) (-1-λ) (i-λ) (-i-λ)
= (λ2-1) (λ2+1)
= λ4-1
Characteristic equation is λ4-1 = 0.
According to Cayley-Hamilton theorem, every matrix satisfies its own characteristic equation, so
A4 = I
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