Answer
a) $0$ b) $3$
Work Step by Step
a) Consider $F=A i+B j+C k$
Then $curl F=\begin{vmatrix}i&j&k\\\dfrac{\partial}{\partial x}&\dfrac{\partial }{\partial y}&\dfrac{\partial }{\partial z}\\A&B&C\end{vmatrix}$
$curl F=[C_y-B_z]i+[A_z-C_z]j+[B_x-A_y]k$
$curl F=[x-x]i+[y-y]j+[z-z]k=0$
b) $div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
$div F=\dfrac{\partial (x+yz)}{\partial x}+\dfrac{\partial (y+xz)}{\partial y}+\dfrac{\partial (z+xy)}{\partial z}=1+1+1=3$
