If $a_{1}, a_{2}, a_{3} . . . . . a_{n}$ are in A.P. Where $a_{i} > 0$ for all i, then the value of
$\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + . . . . . . . . . + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} =$

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If A2=I, then the value of det(A−I) is (where A has order 3)

The correct option is A cannot say anythingA2=I⇒A2−I=O⇒(A−I)(A+I)=O⇒|A−I||A+I|=0∴ Either |A−I|=0 or |A+I|=0Hence, cannot say anything about |A−I|.Hence, option D.

If $A^{2} = I$ , then the value of $d e t (A - I)$ is (where $A$ has order $3$ )

The correct option is A cannot say anything
$A^{2} = I$
$\Rightarrow A^{2} - I = O$
$\Rightarrow (A - I) (A + I) = O$
$\Rightarrow | A - I | | A + I | = 0$
$∴$ Either $| A - I | = 0$ or $| A + I | = 0$
Hence, cannot say anything about $| A - I |$ .
Hence, option D.