Brutus asks Strato to kill him so Brutus wouldn't have to die by the enemies sword
*<edit>
Because the last answer was rather strange I decided to help. Cassius killed himself once he thought his friend (Titinius or something like that) was kidnapped by the enemy. He asked Pindarus (or how ever you spell his name) to kill him. Brutus kills himself later (thanks to the help of Strato) cause he's sure they're are going to lose to Antony. That's how it works in the play Julius Caesar but for all I know the top answer could be true. I rarely look into things deep.
2nd edit
brutus kills himself because he feels bad for killing Caesar for no good reason. Cassius kills himself b/c he thought titunius was kidnapped and dead.
after all this, Antony, octavius and lepidus are in charge of rome
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Cassius convinced Brutus that it was right to kill Caesar and Brutus plots to kill him.
Cassius also wanted to kill Marc Antony, Caesar's closest ally.
Brutus thinks he is just the limb of Caesar but Cassius thinks that they should kill him because he is a tool used by Caesar.
Brutus kills himself, as does cassius.
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