The image shows three group theory problems. I'll transcribe them below:

1. (Not fully visible in the image)
2. Let $G$ be a group and $c, d \in G$. Show that the equation $xc = d$ has a unique solution in $G$.
3. Let $a$ and $b$ be two elements of a group. If the order of $a$ is $d$, then show that the order of $a^{-1}$ is also $d$, and that $o(bab^{-1}) = o(a)$, where $o(a)$ denotes the order of $a$.

Would you like a step-by-step solution for one or both of these problems?

Here are some related questions:

1. What is the definition of the order of an element in a group?
2. How can we prove that every element in a group has an inverse?
3. Why does conjugation preserve the order of elements in a group?
4. What properties must a group satisfy to ensure the uniqueness of solutions?
5. How can the associative property be used in the context of these problems?

Tip: When working with group theory, always keep the basic group properties (associativity, identity, and inverses) in mind—they are key to solving most problems.