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Ironically my show is not to see

A bill that comes with me

Together as is in my group, and has

My box, in me a laugh, though as

I'm neither head of family nor of the state;

In matriarchate.

'Is that irony or coincidence?'
'Coincidentally it is ironic.'

Riddle Answer A Chat

Riddle Explanation
ironically my show is not to see - a chat show.

a bill that comes with me together - a chit chat. A chit is a slip of paper typically used to record an amount of money owed, such as a restaurant bill.

together as is in my group, and has my box - chat groups and chat boxes are some of the terms used in online communication channels.

in me a laugh, though as I'm neither head of family nor of the state; in matriarchate - chat contains the word 'ha', and matriarchate contains 'chat'.