Process behind proving a matrix subgroup is a cyclic subgroup?

Question

I have this matrix below, which is a subgroup of the general linear group with order 3 and over real numbers. I know it is a subgroup, but how can I tell that it is cyclic?

$$K = \begin{bmatrix} 1 & a & b\\ 0 & 1 & c\\ 0 & 0 & 1 \end{bmatrix} | \ a, b, c \in real \ numbers$$

I know that a subgroup is the subgroup $\{ x^n \mid n \in \mathbb{Z} \}$ generated by one of its elements $x \in G$. Would proving that it is cyclic involve multiplying it by itself?

Answer 1

Easiest way to prove this group is not generated by single element is to show it is NOT abelian. Take two specific matrices in this format and multiply them in two different ways to see.