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

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## Question:

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.

**Related Book For**

## Principles of Communications Systems, Modulation and Noise

ISBN: 978-8126556793

7th edition

Authors: Rodger E. Ziemer, William H. Tranter

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