Question 1 - A-Level Maths

State which element is the identity of the group.
Determine the inverse of the element ( $b \circ c$ )
Give a reason why the set $\{ a , b , e , f \}$ cannot be a subgroup of $G$. You must justify your answer.
Show that the set $\{ b , d , f \}$ is a subgroup of $G$.
(ii) Given that $H$ is a group with an element $x$ of order 3 and an element $y$ of order 6 satisfying $$y x = x y ^ { 5 }$$ show that $y ^ { 3 } x y ^ { 3 } x ^ { 2 }$ is the identity element.
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