  Quandles are self-distributive, right-invertible, idempotent algebras. A
group with conjugation for binary operation is an example of a quandle. Given a
quandle $(Q, \ast)$ and a positive integer $n$, define $a\ast_n b = (\cdots
(a\ast \underbrace{b)\ast \cdots )\ast b}_{n}$, where $a, b \in Q$. Then, $(Q,
\ast_n)$ is again a quandle. We set forth the following problem. ``Find $(Q,
\ast)$ such that the sequence $\{(Q, \ast_n)\, :\, n\in \mathbb{Z}^+ \}$ is
made up of pairwise non-isomorphic quandles.'' In this article we find such a
quandle $(Q, \ast)$. We study the general linear group of $2$-by-$2$ matrices
over $\mathbb{C}$ as a quandle under conjugation. Its (algebraically) connected
components, that is, its conjugacy classes, are subquandles of it. We show the
latter are connected as quandles and prove rigidity results about them such as
the dihedral quandle of order $3$ is not a subquandle for most of them. Then we
consider the quandle which is the projective linear group of $2$-by-$2$
matrices over $\mathbb{C}$ with conjugation, and prove it solves the problem
above. In the course of this work we prove a sufficient and necessary condition
for a quandle to be latin. This will reduce significantly the complexity of
algorithms for ascertaining if a quandle is latin.
