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Show that the following are equivalent for matrices P, Q: (1) P, Q, and P + Q are all invertible and (P + Q)-1 =

Show that the following are equivalent for matrices P, Q: 

(1) P, Q, and P + Q are all invertible and (P + Q)-1 = P-1 + Q-1. 

(2) P is invertible and Q = PG where G2 + G + I = 0.

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