Question: Let A and B be symmetric matrices such that A + B = I. Let Z Nn(????,I). a) Prove: If A = A2, then

Let A and B be symmetric matrices such that A + B = I. Let Z ∼ Nn(????,I).

a) Prove: If A = A2, then B = B2 and AB = ????.

b) Prove: If Z′

AZ ∼ ????2 k , then Z′

BZ ∼ ????2 n−k and Z′

AZ ⟂ Z′

BZ.

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