Sorry to be contrary, but I believe you need 2 assumptions for there to be a unique solution. First, that all 3 statements are indeed true. If we allow that one or more of those statements doesn't hold, the whole thing falls apart.
Second, that each cell contains either brass or the key. No empty cells. If you disagree, try looking at these 2 solutions:
Cell 1 = Empty, Cell 2 = Key, Cell 3 = Empty
Cell 1 = Empty, Cell 2 = Empty, Cell 3 = Key
None of the 3 statements apply to either of these, so they're both possible valid solutions and you're left to guess and hope the spiders don't eat your face.
Now, you can brute force your way through by listing all possible solutions and checking which are valid under the given statements. In this case there aren't many possible choices, so that approach is not too bad. However, I'm assuming you're looking for a bit deeper insight, so I'll walk through a technique that can sometimes provide a quicker route to the answer, especially in more complex puzzles.
Since all the implications are one way (they are "if", not "if and only if"), one approach is to start by assuming a condition from the left side of a statement and trace the implications through all the statements to look for inconsistencies.
Just going in order, let's assume first that Cell 3 holds brass. Then by statement 1, Cell 2 holds the key. Since we're assuming key or brass in each and only one key, then Cell 1 would have to be brass. Given that, neither of the last 2 statements apply, so this solution is possible with no contradictions. Let's continue and check the others to be sure we have the only possible valid solution.
Looking at statement 2, let's assume now that Cell 1 holds the key. By statement 2, Cell 3 holds brass. By statement 1, Cell 2 holds the key. Since only 1 cell can hold the key, this is a contradiction. Therefore our original assumption is false, so Cell 1 does not hold the key.
Lastly, look at the third statement. If we assume Cell 2 holds brass, then Cell 1 holds the key. But we already know by our last reasoning that if Cell 1 holds the key we end up with a contradiction. So our assumption here is false, and Cell 2 does not hold brass.
Since Cell 2 cannot hold brass, it must hold the key.