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## Homework Statement

Suppose a linear operator L satisfies <A|L|A> = 0 for every state A. Show that then all matrix elements <B|L|A> = 0, and hence L = 0.

## Homework Equations

##<A|L|A>=L_{AA} and <B|L|A>=L_{BA}##

## The Attempt at a Solution

It seems very straight forward and I don't know how to prove it but here is what I have tried:

##<B|L|A> \to##Using resolution of Identity ##\to \sum_{A} <B|A><A|L|A> \to <B|L|A>=0##

Is it right or do I need to write more.

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