• For 21(a): We have that $n \cdot 5 = 0, 5, 2, 7, 4, 1, 6, 3 \pmod{8}$, and $n \cdot 6 = 0, 6, 4, 2, 0, 6, 4, 2 \pmod{8}$. We see that the set of distinct values of $n \cdot 5$ is $\{0,1,2,3,4,5,6,7\}$, whereas the set of distinct  values of $n \cdot 6$ is $\{0, 2, 4, 6\}$. Note that $\gcd(5,8) = 1$, whereas $\gcd(6,8) = 2 >1$. 
• For 21(b): The numbers that are relatively prime to $8$ are $1,3,5,7$. We see $1^2 \equiv 3^2 \equiv 5^2 \equiv 7^2 \equiv 1 \pmod{8}$. Each number is their own inverse.

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