# If 2 and a b A A b a éù é ù a b = = êú ê ú ëû ë û b a , then

Question:

If $A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]$ and $A^{2}=\left[\begin{array}{cc}\alpha & \beta \\ \beta & \alpha\end{array}\right]$, then

1. $\alpha=2 a b, \beta=a^{2}+b^{2}$

2. $\alpha=a^{2}+b^{2}, \beta=a b$

3. $\alpha=a^{2}+b^{2}, \beta=2 a b$

4. $\alpha=a^{2}+b^{2}, \beta=a^{2}-b^{2}$.

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2005

Solution:

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