(a)  since all the collisions are elastic, so the magnitude of all the impulses is equal and only its directions are different.

since the ball is making a hexagon during the collisions

and the sum of angles of a hexagon is zero.

therefore, total impulse is zero after six impulses.

(b) since velocity changes after each collision, thus linear momentum cant be same.

but the magnitude of velocity is same after collsion only its direction changes.

thus KE remain the same.

but angular momentum cant be same.