I have been trying to figure out the solution to this problem of finding the "velocity" of de-Broglie's wave. I have tried to see answers from countless sources but none of them helped. My book provides me with the solution that : v = (hf)/(mc) Where m is the mass of particle , f is the frequency, h is Planck constant and c is speed of light.

And this came from the fact that they used the formula c = f(lambda)**, which is really absurd to me as to why does the speed of light come here? Shouldn't it be v(wave)= f(lambda). Now I've also read that it has something to do with group velocity of matter waves but none of the sources which I read really explained as to why speed of light should be at play here. Can anyone explain this?

Thanks :)