I've been researching the use of Bayesian linear regression, but I've come to an example that I'm confused about.

Given the model:

$${\bf y} = {\bf \beta}{\bf X} + \bf{\epsilon} $$

Assuming that ${\bf \epsilon} \sim N(0, \phi I)$ and a $p(\beta, \phi) \propto \frac{1}{\phi}$,

How is $p(\beta|\phi, {\bf y})$ reached?

Where: $p(\beta|\phi, {\bf y}) \sim N({\bf X}^{\text{T}}{\bf X})^{-1}{\bf X}^{\text{T}}{\bf y}, \phi ({\bf X}^{\text{T}}{\bf X})^{-1})$.

I've been researching Bayesian linear regression. I'm confused about the following example.

Given the model:

$${\bf y} = {\bf \beta}{\bf X} + \bf{\epsilon} $$

Assuming that ${\bf \epsilon} \sim N(0, \phi I)$ and $p(\beta, \phi) \propto \frac{1}{\phi}$, we have:

$$p(\beta|\phi, {\bf y}) \sim N(({\bf X}^{\text{T}}{\bf X})^{-1}{\bf X}^{\text{T}}{\bf y}, \phi ({\bf X}^{\text{T}}{\bf X})^{-1})$$

How was $p(\beta|\phi, {\bf y})$ determined?