Identify homoleptic complex from following.

Let

$$\begin{aligned} f(x) & =x+a \sqrt{2} \sin x & & , 0 \leq x<\frac{\pi}{4} \\ & =2 x \cot x+b & & \frac{\pi}{4} \leq x<\frac{\pi}{2} \\ & =a \cos 2 x-b \sin x & & \frac{\pi}{2} \leq x \leq \pi \end{aligned}$$

If $$\mathrm{f}(\mathrm{x})$$ is continuous for $$0 \leq \mathrm{x} \leq \pi$$, then

The area of triangle with vertices $$(1,2,0),(1,0, a)$$ and $$(0,3,1)$$ is $$\sqrt{6}$$ sq. units, then the values of '$$a$$' are

If $$A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$$ and $$A$$ adj $$A=A A^T$$, then $$5 a+b=$$