The respective governments of Argentina and Britain.
The former ruling junta in Argentina was unpopular due to the Argentinian people's hatred for General Galtieri's regime, over it's brutal 'dirty war' inside Argentina, the massive human rights violations and a economy in depression with massive debts. Mothers and relatives of those killed off by General Galtieri and his predecessor, General Videla, were holding daily protests demanding that the junta release information concerning those who had vanished at the hands of the junta's hired thugs/killers and the junta looked set to fall.
So General Galtieri hoped to divert public attention away from him by invading the Falklands, it worked for the first month as the junta became popular overnight and most Argentinians put aside their differences and their hatred for the junta to celebrate the capture of the Falklands.
Thatcher, like General Galtieri had a problem with public support, a still weak and unproductive economy in Britain, coupled with roits in London and Liverpool and industrial unrest did not make her popular, the war of course offered her what she needed, a convenient diversion away from the real problems in society by whipping up patriotic sentiment and focusing attention elsewhere.
In the end the gamble paid off for Thatcher and not General Galtieri.
Both Argentine and British lives were lost for no good reason at all, only for political power games.
The only good to have come out of the Falklands War was the downfall of the Argentine junta. Whatever one thinks of Thatcher's governmet, I hated it myself, the junta was way, way worse and it's downfall can only ever be a positive.