Is best case complexity big Omega of worst case complexity?
Consider the following algorithm $A$:

If the input consists entirely of zeroes, return.
Otherwise, count from $1$ to $n^2$, where $n$ is the length of the input.

The best case complexity of this algorithm is $O(n)$, and the worst-case complexity of this algorithm is $\Omega(n^2)$. Does $n = \Omega(n^2)$ hold?