Jee Main 2024 27 01 2024 Shift 2 - Question14
Question 14
If $A$ is a $2 \times 2$ matrix and $I$ is an identity matrix of order $2 \&|A-\lambda|=0$ gives value of $\lambda$ as $-1 \& 3$ then trace of $A^{2}$ is equal to
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Answer: (10)
Solution:
Given $|A-\lambda I|=0$
Value of ’ $\lambda$ ’ are -1 and 3
Now value of ’ $\lambda$ ’ of $A^{2}$ is equal to $\lambda^{2}$
$\therefore \quad$ Let $\lambda _1=(-1)^{2}=1$
$$ \lambda _2=(3)^{2}=9 $$
Trace of $A^{2}=1+9$
$$ =10 $$
$\therefore$ Answer is 10
BETA
