Whilst in most cases, I'm clear using who or whom but this is one of the sentences bothering me! 

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> Whom/who did she invite? 
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Whom did she invite looks very very natural to me. The general rule (this will work in most of the cases, no exceptions please!) I remember is... *be yourself* in that situation, and **if 'I' fits, it'll be 'who' and if 'me' fits, it'll be 'whom'.** 

Some examples where this rule works as a breakthrough...

> 
> **Whom** this matter is concerned to? - The matter is concerned to **me** and not **I** so *whom!*   
>  Our madam wondered **who** broke the glass - **I** broke the glass and not **me** so *who!*
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That way, *She invited **me** and not **I** so it should be - **whom** did she invite, shouldn't it?* Also, if you take it other way - She invited *him* and not *he*.