If $A=\left[\begin{array}{cc}1+2 i & i \\ -i & 1-2 i\end{array}\right]$, where $i=\sqrt{-1}$, then $A(\operatorname{adj} A)=\ldots$

Which of the following statements is contingency?

$$\int_\limits a^b \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a+b-x}} d x=\ldots \ldots$$

The intercept on the line $y=x$ by the circle $x^2+y^2-2 x=0$ is $A B$. The equation of the circle with $A B$ as a diameter is .............