Let $W$ and $B$ be two Brownian motions with $\text{d}\langle W, B\rangle_t = \rho \text{d}t$ under some probability measure $\mathbb{P}$, where $\rho$ is a constant.
Let $\mathbb{Q}$ be an equivalent measure to $\mathbb{P}$. Does $\text{d}\langle W, B\rangle_t = \rho \text{d}t$ under $\mathbb{Q}$? I think this is true by Girsanov?