#### Answer

a). Linking of arms by the two skaters moving in opposite direction is similar to head-on collision and hence the angular momentum will remain same.
So, $mv-mv=mv^{'}$
Hence, $v^{'}=0$
Hence, the velocity of their center of mass after they link arms will be zero.
b). Their initial linear kinetic energies would be converted and the two skaters would start to rotate about the combined center of mass.