Prove that $b\cdot\aleph_0=b$, where b is an infinite set.

Question

Prove that $b\cdot\aleph_0=b$, where $b$ is an infinite set. I tried by multiplying $1\le\aleph_0\le b$ with $b$ but then I have to prove that $b\cdot b=b$ and that seems harder than my original problem.