Positive square root of $BB^{t}$ is non-singular

Question

This is the problem form Kreyszig's book (Introductory Functional Analysis) sec. 9.4 Problem 8

Let $B$ be a nonsingular $n$-rowed real square matrix and $C=BB^{t}$. Show that $C$ has a nonsingular positive square root $A$.

My problem is how to prove that $A$ is nonsingular!

Any help would be appreciated.

Thank so much