Yes, you are entitled to live, study and work in Portugal once you have been issued a Golden visa – residence permit for investment activity (ARI). Family members can also work in Portugal until the expiry of the golden visa. However you cannot work in other EU member states (permission required). Golden visa holders enjoy visa free movement in Europe’s schengen area for a period of 90 days in 180 days period for tourism, business, visiting family and friends.
If you have EU permanent residence permit from Portugal, you can work in another EU countries by applying for a separate residence permit for work (depends on labour market conditions and quotas).
Applying for Portuguese Citizenship get you unrestricted access to EU. For example, if you have Portuguese citizenship, you can work anywhere in the EU .