7. Consider the subset $U_8 = \{1, 3, 5, 7\}$ of $Z_8$ which is a group under multiplication. Let $f: U_8 \to \mathbb{Z}_2 \times \mathbb{Z}_2$ be defined by $f(1) = (0, 0)$; $f(3) = (1, 0)$; $f(5) = (0, 1)$; $f(7) = (1, 1)$. Then show that $f$ is an isomorphism