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**1. Homework Statement**

I need to prove two things about the Catalan numbers. The first is that Cn is odd iff n=(2^k)-1 for some positive integer k.

The second is that given the matrix A defined by the rule a(i,j)=C(i+j), prove that det A=1. I have not covered determinants in my linear class yet, so I do not have any idea what to do with this one.

**2. Homework Equations**

**3. The Attempt at a Solution**

I am assuming that both proceed by induction. The first one seems to be more direct, but I am really lost as to how to proceed with both. Any help or suggestions is greatly appreciated. Thanks a lot!