Prove $\mathbb{Q}$-subalgebra of quaternions is a division algebra over $\mathbb{Q}$

Question

Let D be the $\mathbb{Q}$-subalgebra of $\mathbb{H}$ having basis $1, i, j, k$. Prove that D is a division algebra over $\mathbb{Q}$. This is an exercise from Rotman's Algebra. I only see that is to prove D is a division ring regarded as an algebra over its center $\mathbb{Q}$ by definition. And I know the quaternions $\mathbb{H}$ is a 4-dimensional vector space over $\mathbb{R}$ with basis $1, i, j, k$. The hint in the book is: Compute the center $Z(D)$. Thanks in advance for any help!