How to impose restrictions on a random matrix via its prior distribution?

I am reading the paper Factor analysis and outliers: A Bayesian approach. The author starts with a factor analysis model given by
$${bf y}_i = {bf Lambda} {bf z}_i + {bf e}_i, quad i = 1, ldots, n,$$
where each ${bf y}_i$ is a $p$-dimensional observation vector, each ${bf z}_i$ is a $K$-dimensional latent factor vector, and ${bf Lambda}$ is a $p times K$ full-rank matrix of factor loadings. The author assumes that the factors and the error term are Normal:
$${bf z}_i sim mathcal{N} ({bf 0}, {bf Phi})$$
$${bf e}_i sim mathcal{N} ({bf 0}, {bf Psi})$$

The author assigns Wishart priors to ${bf Phi}^{-1}$ and ${bf Psi}^{-1}$:
$${bf Phi}^{-1} sim mathcal{W}_K left( {bf Phi}_{*}, nu_{*} right)$$
$${bf Psi}^{-1} sim mathcal{W}_p left( {bf Psi}_{*}, n_{*} right)$$

In the paper the author writes something I found to be quite interesting:

While classical factor analysis sets $bf Phi = I$ and uses a diagonal $bf Psi$ matrix, we impose these restrictions via the prior information matrices ${bf Psi}_{*}$ and ${bf Phi}_{*}$.

Question: What should the values of ${bf Psi}_{*}$ and ${bf Phi}_{*}$ be in order to do what the author is suggesting?

The author does not seem to state exactly how this can be done, but I may have missed it so I will continue reading it. My own research on this matter pointed me to these seemingly similar unanswered questions here and here.

---

UPDATE: I did some research on the Wishart distribution and if you specify that $Psi_*$ and $Phi_*$ are two diagonal matrices, then $mathbb{E} [Psi]$ and $mathbb{E} [Phi]$ will be two diagonal mean matrices. Perhaps, this is what the author is referring to. Still unsure, though.

UPDATE 2: I set $Psi_*$ and $Phi_*$ to diagonal matrices and ran simulations in R, but the results aren’t what I expected. The simulated values I obtained are not diagonal, so I think I misinterpreted the author’s statement. I thought that if you formulate the factor analysis model with the prior distributions above, that you can consider it the classical factor analysis model by choosing certain hyper-parameter value. But it seems that this formulation does not produce the classical factor analysis model.

UPDATE 3: The classical factor analysis model sets ${bf Phi} = {bf I}$ (i.e. non-random), sets $bf Psi$ to be a diagonal matrix (i.e. random diagonal matrix) and assigns prior distributions to only the diagonal elements. What I understand the author’s statement to mean, is that I can do the aforementioned things by using Wishart priors on $bf Phi$ and $bf Psi$ with special scale matrices $bf Phi_*$ and $bf Psi_*$.