Electro, women and girls make up 50.2% of the total population (Census 2006). What percentage of Ireland's wealth is owned by women? What percentage of the workforce are they? What percentage of businesses are owned by women? What percentage of companies are headed by women? What percentage of elected representatives are women? What percentage of judges are women?
Basically I'm asking you to supply some statistics which prove your contention that Ireland is now a matriarchy.
If you can show that women own more of Ireland's wealth than men do, participate in the labour force more than men, own and control more companies than men and are more likely to make the laws (either as elected representative/judges) and develop public policy than men, then you'll have proved yourself right.
If you can't then you're just another whinger.