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**First question:**If A is pd, then A^-1 is pd.

Outline of answer:

- If A is pd, then there exists a nonsingular matrix P st A=P'P
- Then A^-1 = (P'P)^-1 = (P^-1) * (P^-1)' = (P^-1)' * (P^-1)

**Second question:**If rank(A

_{nxp}) = p<n, then A'A is pd.

Outline of answer:

- x'(A'A)x = (Ax)'(Ax)
- (Ax)'(Ax) is a sum of squares which is > 0 as long as Ax does not = 0

Thanks =)

**EDIT:**I think I figured it out if anyone wants me to post the answers. I deleted the attempts since they look plain stupid in retrospect

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