Prove that if $A=BQ$ then $A=B$

Question

I'm having some trouble with a question in my linear algebra textbook:

Let $A$ and $B$ be positive definite matrices, and let $Q$ be a unitary matrix. Prove that if $A=BQ$, then $A=B$.

I tried to play around with the given equality, but I'm not getting any results. Tips would be appreciated:)

Answer 1

Hint: If $A = BQ$, then $AA^* = BQ(BQ)^*$.