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Prior distribution importance in Bayesian inference

I am performing a Bayesian multivariate regression, and therefore I have to construct the prior and the subsequent posterior.

But the paper that I am using as a reference, uses a "Uninformative prior", and moreover, gives me directly the expression of the posterior.

So what I did, was just drawing from the posterior directly, without considering the prior at all.

A detail of what I meant is this: enter image description here

I just draw from the posterior (so the last two expressions).

I didn't understood the meaning of uninformative prior, and if, since it gives me no information, I can "skip it" and use directly the posterior derived from it.

Let me know if my reasoning is correct, or if you can suggest me how to incorporate the prior (how is that distribution defined??)

Thanks in advance